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Fall2021MathGymStudentWorkbook.pdf

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FLORIDA INTERNATIONAL UNIVERSITY

MATH GYM STUDENT WORKBOOK

Fall 2021

Table of Contents

WELCOME NOTE……………………………………………………………………………………………………………………2 TOPICS FOR FALL 2021 ……………………………………………………………………………………………………..3 MAC 1105 MATH GYM FALL 2021 WEEK 1 AND WEEK 2……………………………………………………6 MAC 1105 MATH GYM FALL 2021 WEEK 3………………………………………………………………………13 MAC 1105 MATH GYM FALL 2021 WEEK 4………………………………………………………………………16 MAC 1105 MATH GYM FALL 2021 WEEK 5………………………………………………………………………19 MAC 1105 MATH GYM FALL 2021 WEEK 6………………………………………………………………………23 MAC 1105 MATH GYM FALL 2021 WEEK 7………………………………………………………………………28 MAC 1105 MATH GYM FALL 2021 WEEK 8………………………………………………………………………31 MAC 1105 MATH GYM FALL 2021 WEEK 9………………………………………………………………………35 MAC 1105 MATH GYM FALL 2021 WEEK 10……………………………………………………………………38 MAC 1105 MATH GYM FALL 2021 WEEK 11……………………………………………………………………40 MAC 1105 MATH GYM FALL 2021 WEEK 12……………………………………………………………………42 MAC 1105 MATH GYM FALL 2021 WEEK 13……………………………………………………………………46 MAC 1105 MATH GYM FALL 2021 WEEK 14……………………………………………………………………49 MAC 1105 MATH GYM FALL 2021 WEEK 15……………………………………………………………………51

WELCOME NOTE Welcome to Math Gym. This element of your College Algebra course is designed to provide you with the

opportunity to gain more in-depth understanding of the concepts involved in the course, as well as

provide you with the chance to work collaboratively with your peers and engage with Mathematical

processes. While the Lab gives you the chance to practice skills of algebraic manipulation and test your

conceptual understanding frequently by combining multiple concepts into one problem, the math gym

problems will ask you to think deeply about the concepts and use your own words to explain that

thinking. Also, throughout the workbook you will work on questions you may see in future classes.

How Math Gym operates:

• Once you signed up for a Math Gym, you will continue to meet each week at that Math gym

• You are to complete the Math Gym worksheet for that respective week prior to attending each Math

Gym. If you cannot answer a question, write what about the question is difficult, be specific.

• For Virtual Gyms: You must upload the complete worksheet for that respective week via google

classroom. You LA will provide the link to your respective google classroom

You must have a working webcam and microphone to enter your Math Gym. Your cam must remain on

at all times, while you are in the math gym session

• You and your classmates will share your work, defend your answers and pose questions to each other

and your LA

• Concept maps and/or challenge questions will be graded for clarity and correctness. A grade of 0%

represents minimal effort and/or inconsistent or incoherent work. A grade of 50% represents work that

shows effort to fully answer the question being asked but lacks the mathematical accuracy or cohesion.

A grade of 100% represents an answer that attempts to fully address the intent of the problem and is

mathematically coherent

• If you miss a Math Gym for an excused absence, you need to speak to your professor (not LA) to ensure

that the excuse is accepted.

• It is expected that the work in Math Gym be done in groups. Your LA may have to move you in order to

maximize the effectiveness of the learning environment

• Bring your own questions to Math Gym. Ask “why” a lot. Be on time and attend every week!

The Math Gym questions are designed to get at the meaning of the Math. If something does not make

sense, or you are doing a step just because that is a step that you saw someone else do (teacher, LA,

peer, help me solve this) then ask for help. Math makes sense-always.

All of us here in the Mastery Math Lab wish you all the best for this semester and hope to be able to

help you on your journey of understanding.

TOPICS FOR FALL 2021

Fall 2021 Week

Starting Topics (Sections – Blitzer)

Week 1 8/23

Pre-Class Assignment: Functions In-Class: Functions (2.1) Functional Notation (2.1) Domain and Range (2.1)

Week 2 8/30

Pre-Class Assignment: Multiple representations of functions In-Class: Graphs of Functions (2.1) Properties of Functions (2.2)

Week 3 9/6

Scheduling period for Test 1: Pre-Class Assignment: Library of Functions In-Class: Graphing Techniques (2.5)

Week 4 9/13

Test 1 in Math Lab (2.1, 2.2, and 2.5)

Pre-Class Assignment: Introduction to piece wise functions and Average rate of change. In-Class: Piecewise Functions (2.2) Average rate of change (2.5)

Week 5 9/20

Pre-Class Assignment: Find Sum, Difference, Product of Functions In-Class: Quotient of Functions (2.6) Composition of Functions (2.6) Difference Quotient (2.2)

Week 6 9/27

Pre-Class Assignment: Graph of a Quadratic Function Intro In-Class: Quadratic functions and Their Graphs (3.1), Mathematical Models (3.1) to Graphing Techniques (2.5)

Week 7 10/4

Scheduling period for Test 2

Fall 2021 Week

Starting Topics (Sections – Blitzer)

Pre-Class Assignment: Domain of Rational Functions In-Class: Rational Functions: Domain, Asymptotes, and Graph (3.5)

Week 8 10/11

Test 2 in Lab (2.2, 2.5, 2.6, 3.1, 3.5) Pre-Class Assignment: Solving from Graph In-Class: Solving Polynomial and Rational Inequalities (3.6)

Week 9 10/18

Pre-Class Assignment: Basics of one-to-one In-Class: One-to-one Functions (2.7) Inverse Functions (2.7)

Week 10 10/25

Scheduling period for Test 3 Pre-Class Assignment: Exponential Exercise In-Class: Exponential Functions (4.1), Basic Exponential Equations (4.4)

Week 11 11/1

Last day to Drop is Monday, 11/2 at 11:59pm Test 3 in Lab (2.7, 3.6, 4.1, 4.4)

Pre-Class Assignment: Finding the inverse of the exponential function In-Class: Logarithmic Functions (4.2), Domain, Natural Log, Graphs,

Week 12 11/8

Pre-Class Assignment: Rules of exponents and properties of logs In-Class: Properties of Logarithms (4.3), Solving Exponential and Logarithmic Equations (4.4)

Week 13 11/15

Pre-Class Assignment: Pythagorean Theorem In-Class: Exponential Modeling (4.5) Midpoint and Distance Formulas (2.8) Circles (2.8)

Fall 2021 Week

Starting Topics (Sections – Blitzer)

Week 14 11/22

Scheduling period for Test 4 Pre-Class Assignment: Systems of Linear Equations In-Class: Systems of Non-Linear Equations (8.4) Solving Quadratics over Imaginary Numbers (1.5)

Week 15 11/29

Test 4 in Lab (4.2, 4.3, 4.4, 4.5,2.8 )

Review for Final Exam

Week- 16 12/6 Final Exam: Comprehensive (Scheduled in the lab. Same way as tests.)

MAC 1105 MATH GYM FALL 2021 WEEK 2

1. Sometimes we make mistakes out of carelessness or moving too quickly, but sometimes it is because we are not really sure what we are doing and are simply trying to “match” a similar looking example. This means that we do not understand the mathematical meaning in the problem. Write down an example of a mistake you made on the homework /quizzes: What do you need to know/understand so that you will not make this mistake again? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________

Goals for week 1 and week 2

Check if you understand:

□ What it means to be a function

□ The 3 main ways a function may be represented; verbally,

graphically and algebraically

□ What the domain of a function means

□ What the range of a function means

□ The different properties of a function

□ What it means to be the graph of a function

Check if you are able to:

□ Find the domain of a function

□ The range of a function

□ How to graph a function

□ Identify intervals of decreasing, increasing or constant on the

graph of a function

□ Identify relative maxima or minima on the graph of a function

□ Identify odd or even functions and their respective symmetries

2. Your younger cousin saw you working on “My Labs Plus” and saw the word “function”. Curious they

ask you, “What is a function?” explain to them, in detail, what is a function.

______________________________________________________________________________

After your explanation your cousin says, “Wow you have a lot of questions on functions! Why

are functions so important anyway?” Explain the importance of functions to your cousin.

______________________________________________________________________________

3. What does it mean for when someone asks where a function is not defined? Give an example

______________________________________________________________________________

Explain what the domain of a function is

______________________________________________________________________________

4. Someone claims that the fuel efficiency (miles per gallon of a car) is an example of a function.

a) Make a reasonable argument why fuel efficiency is a function

______________________________________________________________________________

b) Make a reasonable argument why fuel efficiency is not a function

______________________________________________________________________________

c) Which side of the argument do you agree with?

5. The graph of a function is a picture representation of that function. All the x values (input values) on

the graph also known as the _____________ give all corresponding y values (output values) on the

graph also known as the ____________.

How can we use this idea to find out if a given point is on the graph of a given function?

______________________________________________________________________________

6. a) Graph the function 𝑓(𝑥) = 2𝑥 − 1

What type of function is 𝑓(𝑥) = 2𝑥 − 1

__________________________________________________

b) Show on the graph as well as algebraically that the following points belong to 𝑓(𝑥). If a

coordinate is missing, show how you can find the missing coordinate.

(1, 4) (x, -7) (0, y)

7. Let f(x)=(3x)2 and g(x)=9x2

a) Find f (2) and g (2)

b) Find f (-2) and g (-2)

c) Are f and g equivalent functions? Why or why not?

___________________________________________________________________________ ___________________________________________________________________________ d) Let f(k) =k+6 and g (k) =k+6. Are f and g equivalent functions? Why or why not?

___________________________________________________________________________

Facts/Characteristics: Expressions may consist of multiple terms. We can add or subtract expressions by combining like terms. We can also multiply and divide expressions using properties of

exponents or factoring to simplify completely.

Concept Map During every class meeting your professor will cover key concepts that are important for your course. It is critical that you identify these concepts and actively work toward understanding their connections to other previous mathematical topics and ideas. A concept map is a great way to make and organize these connections, and is very useful when you want to review for an exam. Every week before your math gym, you will be required to create a concept map based on the topics already covered in your College Algebra class during that same week. You may select any of the key concepts covered that week to produce your map; some weeks, however, there will be only one key concept covered. You may use the schedule of topics that is included for you here in the packet (the same topics that are in your syllabus) as a guide to the key concepts that will be covered every week. For the first few weeks we will provide you the concepts that were taught, and you can use these to design your concept map. Going forward, you will need to know how to recognize and locate concepts on your own. If you are struggling identifying concepts, talk with your professor or any of the LAs in the lab. During math gym, compare your maps with your math gym classmates and correct the map when you find any misconceptions. Write your work in the provided boxes as neatly as possible (pencil works best). Note you will not receive credit if your work is not presented in a clear manner. Here is an example of a concept map from a week one topic. Note that the key concept is at the center of the map:

Expressions

Definition (in your own words): A single term or more than one term containing variables or constants or operations between values. There is no equal sign.

Examples: 𝑥2

7𝑧 − 25

𝑘3 − √2

Non-Examples:

𝑥 − 13 = 4

ℎ2 + ℎ = 0

Using the provided list, create a concept map for two of the topics taught in weeks 1 and 2.

List: Functions, Functional Notation, Domain, Range, and Graphs. Don’t forget to compare your maps

and make corrections in order to receive full credit.

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

MAC 1105 MATH GYM FALL 2021 Week 3

1. If the graph of the function f(x)= cos(x) looks like

Use the coordinate system below to graph g(x) = cos (x+ π/2).

Goals for week 3

Check if you understand:

□ What it means to transform a graph

Check if you are able to:

□ Recall the library of functions and their respective graphs

□ Identify functions by their respective graph

□ Transform points of a graph

□ Transform entire graphs

One of your classmates is confused and says “but I have never seen cos(x) before” …you say “it does not

matter; you already know how to do this because we just…” Complete this statement to help your

classmate understand why they already know how to get the graph of cos(x+ π/2) using

transformations.

______________________________________________________________________________

2. Draw a parabola with at least 3 transformations from the parent function. Write the function for your parabola. Note that your parabola should contain distinct points rather than be a sketch or approximation. (At least 3 points)

Your function:

How do you know that your function matches your graph?

_______________________________________________

Concept map. List of topics: Library of Functions, and Transformations on Functions.

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

MAC 1105 MATH GYM FALL 2021 Week 4

1. Given the following 𝑓(𝑥) = { −|𝑥| + 1 𝑤ℎ𝑒𝑛 𝑥 < −2 6 𝑤ℎ𝑒𝑛 − 2 ≤ 𝑥 ≤ 3 (𝑥 − 3)2 + 2 𝑤ℎ𝑒𝑛 3 < 𝑥

Is 𝑓(𝑥) a function? Explain how you know.

______________________________________________________________________________

For 𝑓(𝑥):

What are the intercepts?

What is the domain?

What is the range?

Goals for week 4

Check if you understand:

□ What it means to be a piecewise function

□ How to use a piecewise function

Check if you are able to:

□ Create a piecewise function

□ Find the domain and range of a piecewise function

□ Compute the average rate of change of a function on an interval

Graph f(x):

Concept Map: There was one key concept introduced this week, what was it? Create a map for that

concept.

The Key concept was: __________________________________________________________

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

MAC 1105 MATH GYM FALL 2021 Week 5

1. Given the table of values, find the outputs of the given compositions for the given inputs.

X -3 -2 -1 0 1 2 3

f(x) 11 9 7 5 3 1 -1

g(x) 8 -3 0 1 0 -3 -8

f◦g (1) = _______ g◦f (3)=_______ f◦g (2) =_______ f◦f(3)=_______ f◦g (-1) =_______ g◦g (1)=_______

Goals for week 5

Check if you understand:

□ What it means to be a composite function

Check if you are able to:

□ Find the sum, difference, product and quotient of functions

□ Form a composite function

□ Find the domain and range of a composite function

□ Find and simplify the difference quotient of a function

2. Given 𝑓(𝑥) = −2𝑥 2 − 3𝑥 + 1 a. Find and simplify the difference quotient

Initial Evaluation: Write what you expect your final answer to look like:

Write down each step

Explain why your step gets you closer to

an answer

Final Evaluation: Did your final answer match what you expected in your initial

evaluation?

Concept Map: Choose a key concept for this week (Operations on Functions, Composite Functions,

Difference Quotient), and create a concept map for that key concept.

The Key concept was: __________________________________________________________

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

Extra credit Challenge Question:

The resistance of blood flow in a blood vessel (R) is inversely proportional to the fourth power of the

radius (r) of the respective blood vessel

a. Build a function based on the given information.

b. What would be the domain of the function you created? (Remember to think in terms of

this question). Give answer in interval notation

c. In terms of this question, describe in words what the dependent variable of the function you

created is _________________________________________________________

d. In terms of this question, describe in words what the independent variable of the function

you created is __________________________________________________

e. Based on the function you created, describe why it is or isn’t possible to have a blood vessel

that has zero (0) resistances of blood flow

________________________________________________________________________

f. Graph the function you created.

MAC 1105 MATH GYM FALL 2021 Week 6

1. The Revenue, in dollars, is equal to the unit selling price, p, of the product, times the number x

of units sold. Suppose that p and x are related by: 𝑝(𝑥) = − 1

4 𝑥 + 3.

a. What does the function p(x) represents? ___________________________________________________________________________ ___________________________________________________________________________

Goals for week 6

Check if you understand:

□ The characteristics of a quadratic function

□ The characteristics of a parabola

Check if you are able to:

□ Graph a parabola

□ Determine the minimum and maximum of a quadratic function

□ Solve problems involving the minimum and maximum of a

quadratics function

b. Express the Revenue as a function of the number x of units sold and as a function of price.

What do you expect your final answers to look like?

Why?

Revenue as a function of the number of units sold:

Why did you do it that way

Revenue as a function of price:

Why did you do it that way

Someone in your math gym says “I do not know what is meant when they write ‘is a function

of”, several others agree. What do you understand is meant by this phrase?

2. Given that 𝑓(𝑥) = 2𝑥2 + 4𝑥 − 1 a. Find the domain of 𝑓(𝑥)

b. range of 𝑓(𝑥)

c. x-intercepts

d. y-intercept

e. Represent the function 𝑓(𝑥) in vertex form

f. Once in standard form, identify the transformations of 𝑓(𝑥) in the correct order.

g. Graph 𝑓(𝑥) = 2𝑥2 + 4𝑥 − 1

Concept Map: What was the key concept this week? Create a concept map for that key

concept.

The Key concept was: __________________________________________________________

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

Challenge Questions (extra credit). This must be submitted on google classroom before the start of

math gym to receive credit.

In studying genetics, you will learn of the Hardy-Weinberg principle (also known as Hardy-Weinberg equilibrium). This rule allows us to predict gene frequencies between generations given specific assumptions (random mating, no mutations, infinite population size, no genetic migration and no natural section)

a. Some genes have more than one form. These forms are called alleles. The sum of the frequencies of all of the alleles of a gene must equal 1. Why is this? ___________________________________________________________________________

___________________________________________________________________________

b. This means if allele K has a frequency of p and allele C has a frequency of q then ___________________________________________________________________________

A genotype is a possible combination of alleles. So in our example of allele K and allele C, if the Hardy- Weinberg assumptions are true the possible combinations of alleles are KK, CK, KC, and CC. Note that genetically speaking, CK and KC are identical.

c. If allele K has a probability of p and allele C has a probability of q what is:

the probability of getting genotype KK? __________

the probability of getting genotype CK? __________

the probability of getting genotype KC? __________

the probability of getting genotype CC? __________

d. Now, using your knowledge of probability, all of the possible genotype outcomes listed above and math, what is the sum of all genotype probabilities in this example? (You may want to refer to your conclusion about the sum of all allele probabilities) ______________________________________________________________________________ ________________________________________________________________________ e. Write the algebraic equation that expresses the sum of the genotype probabilities.

f. In a given population the frequency of allele K=p and frequency of allele C=q.

From a sample of 100,000 persons, 35,000 persons have genotype KK

Calculate the number of persons with genotype KC as well as CC

MAC 1105 MATH GYM FALL 2021 Week 7

1. Explain step by step how to graph the function 𝑔(𝑥) = 1 − 2

𝑥 starting with the parent function

and showing each transformation in the correct order and give the final graph.

a. Parent Function:

b. The first transformation is a:

And the equation for the transformation is

c. The second transformation is a:

And the equation for the transformation is

d. The last transformation is a:

And the equation for the transformation is

Continued on the following page

Goals for week 7

Check if you understand:

□ What it means to be a rational function

□ What are the features of rational functions

Check if you are able to:

□ Find the domain and range of rational functions

□ Graph a rational function

□ Transform rational functions

□ Solve applied problems that model rational functions

Graph 𝑔(𝑥)

2. On a pre-calculus quiz, your friend was asked the following question; “describe in words what the vertical asymptote of a rational function is”. Your friend answered, “the vertical asymptote of a rational function is the domain of the function.” Your friend does not understand why their answer was marked incorrect. Explain to your friend the difference between the vertical asymptote and the domain of a rational function. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

Concept Map: List the key concept for this week and create a concept map for that key

concept.

The Key concept was: ________________________________________________________

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

MAC 1105 MATH GYM FALL 2021 Week 8

1. You completed exam two for this course. Are you happy with the grade you earned in test two?

______________________________________________________________________________

If you are unsatisfied with the results, what are you going to do differently that can help

improve your grade?

______________________________________________________________________________

If you are happy with the grade, what are you doing that gave you that good grade?

______________________________________________________________________________

What can you do to improve on that good grade you earned on test two?

______________________________________________________________________________

If you made changes in your study habits after test one and you earned a grade that you are not

happy with in test two; please talk with your LA (or any LA in the Lab), or your professor. We are here to

help you, use us.

Goals for week 8

Check if you understand:

□ What is a polynomial or rational inequality

Check if you are able to:

□ Solve a polynomial inequality

□ Solve a rational inequality

□ Solve questions that model polynomial and rational inequalities

2. Given 𝑓(𝑥) = 𝑥2 − 4𝑥 + 3. 𝐹𝑖𝑛𝑑 𝑤ℎ𝑒𝑛 𝑓(𝑥) ≤ 0

a) Solve by graphing and write down the answer using interval notation.

Solution

b) Solve 𝑓(𝑥) ≤ 0 algebraically. Write solution in interval notation.

3. Given 𝑓(𝑥) = 3

𝑥+2 − 1. Find when 𝑓(𝑥) ≤ 0

a. Solve by graphing and write down the answer using interval notation.

b. Solve 𝑓(𝑥) ≤ 0 algebraically. Write solution in interval notation.

Concept Map: List the key concept for this week and create a concept map for that key

concept.

The Key concept was:

__________________________________________________________

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

MAC 1105 MATH GYM FALL 2021 Week 9

1. On the coordinate system below, plot the following pairs of points:

(3, 1), (6, 5), (-2, -4), (5, 6), (-4, -2), (1, 3)

a) What can you say about this group of

coordinate points?

b) What can you say about the position of these

points on the coordinate system?

c) How can you use the conclusion from b to help you in other problems?

Goals for week 9

Check if you understand:

□ What it means for a function to be one-to-one

□ What it means for a function to have an inverse

Check if you are able to:

□ Find the inverse of function

□ Find domain and range for inverse functions

2. Given the function 𝑓(𝑥) = (𝑥 + 4)(𝑥 − 2).

a. Graph the function 𝑓(𝑥) = (𝑥 + 4)(𝑥 − 2). Using what you did in number 1, graph 𝑓 −1(𝑥)

b. Is 𝑓 −1(𝑥) a function? Yes or No (circle one) Explain:

______________________________________________________________________________

c. If a function does not pass the horizontal line test, then its inverse will not pass

the_____________________ line test

3. The domain of a one-to-one function f is [5, ∞) and its range is (2, ∞). State the domain and

range of 𝑓 −1.

Concept Map: List the key concept for this week and create a concept map for that key concept.

The Key concept was: __________________________________________________________

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

MAC 1105 MATH GYM FALL 2021 Week 10

1. A friend of yours was trying to do the following problems but forgot what an exponential

equation means. Help your friend understand the equations. a) 𝑒 4 = 𝑀

Express the equation using words ____________________________________________________________________ ____________________________________________________________________

b) 49 = 72

Express the equation using words ____________________________________________________________________ ____________________________________________________________________

Goals for week 10

Check if you understand:

□ What it means to be an exponential function

□ The properties of an exponential function

Check if you are able to:

□ Find the domain and range of exponential functions

□ Graph exponential functions

□ Transform exponential functions

□ Answer questions that model exponential functions

Concept Map: List the key concept for this week and create a concept map for that key concept.

The Key concept was: __________________________________________________________

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

MAC 1105 MATH GYM FALL 2021 Week 11

1. Change each logarithmic statement to an equivalent statement involving an exponent

a) ln 𝑥 = 5 is the same as: ______________________________________ Express the same relationship using words_______________________ __________________________________________________________ __________________________________________________________

b) log 𝑥 = 3 is the same as: _____________________________________

__________________________________________________________ Express the same relationship using words_______________________ __________________________________________________________ __________________________________________________________

Change each exponential statement to an equivalent statement involving a logarithm i. 4𝑥 = 16 is the same as: ________________________________________

Express the same relationship using words________________________ __________________________________________________________

ii. 𝜋 𝑥 = 𝑍 is the same as: _______________________________________ __________________________________________________________

Express the same relationship using words_______________________

__________________________________________________________

Goals for week 11

Check if you understand:

□ What it means to be a logarithmic function

□ How exponential and logarithmic functions are connected

Check if you are able to:

□ Find the domain and range of logarithmic functions

□ Answer questions that model logarithmic functions

Concept Map: List the key concept for this week and create a concept map for that key concept. The Key concept was: __________________________________________________________

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

MAC 1105 MATH GYM FALL 2021 Week 12

Goals for week 12

Check if you understand:

□ How to manipulate logarithmic equations

□ The connection between rules of exponents and properties of logs

Check if you are able to:

□ Graph logarithmic functions

□ Transform logarithmic functions

□ Solve log equations using the different properties of logs

Consider the following function 𝑓(𝑥) = log2(𝑥)

Evaluation: Describe in words what the graph will look like.

State the function’s domain, range and asymptotes.

How would the domain, range, and asymptote change for

𝑓(𝑥) = log2 𝑥 − 5 ________________________ _________________________________________

_________________________________________

𝑓(𝑥) = log2(𝑥 − 5)_____________________ _________________________________________

_________________________________________

𝑓(𝑥) = −log2 𝑥__________________________ _________________________________________

_________________________________________

Graph the function 𝑓(𝑥) = 𝑙𝑜𝑔2(𝑥) and its inverse 𝑓 −1(𝑥) using

a least 3 points for each and the associated asymptotes.

Find 𝑓 −1(𝑥) showing each step.

Find the domain of the function 𝑓(𝑥) = −2 log5(𝑥 − 5) − 3.

Was this domain difficult to find? If so, why? If not, why might someone else find it difficult?

List the transformations in their correct order, starting with the parent function

a) Parent function:

b) Frist transformation

c) Second transformation

d) Third transformation

e) Fourth transformation

Concept Map: List the two key concepts for this week and create concept maps for them.

The Key concepts are: __________________________________________________________

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

MAC 1105 MATH GYM FALL 2021 Week 13

1. You are given the two endpoints of a line segment, (-4,6) and (7,6)

a) Graph the two end points

Goals for week 13

Check if you understand:

□ How the distance formula is used to describe a circle

Check if you are able to:

□ Find the distance of two end points of a line segment

□ Find the midpoint of a line segment

□ Write the standard form of a circle

□ State the center and radius for a circle that is in its standard form

□ Investigate exponential modeling of real-life phenomena

b) What is the x coordinate that is exactly between the two end points?

c) Find the average of the two x coordinates and compare it to your answer in part b)

d) What is the y coordinate that corresponds to the middle x coordinate you found in part b)

e) Find average of the two y coordinates and compare it to your answer in part d)

f) What is the coordinate for the point that is in the middle of the endpoints (-4,6) and (7,6)?

g) We call the point that is in the middle of the endpoints (-4,6) and (7,6) the

__________________ of the line segment.

2. You are given the endpoints of a line segment (5,2) and (7, 10)

a) Show how you would find the midpoint of the line segment. If you are using a formula, first

write the formula out and show each step.

b) How does finding the x coordinate and the y coordinate in the formula you used above

compare to the way you found the average in part c) and e) of questions 1?

c) Based on your work in question 3 and 4, what conclusion can you make about the midpoint

formula? ___________________________________________________________________

Concept Map: List the key concept for this week and create a concept map for that key concept.

The Key concept was: __________________________________________________________

Definition (in your own words)

_________________________________________________

Facts/Characteristics

_________________________________________________

Examples Counter Examples

MAC 1105 MATH GYM FALL 2021 Week 14

Use a graph to solve the following system of equations.

2𝑥2 − 𝑦 = 0

Goals for week 14

Check if you understand:

□ What are nonlinear system of equations

Check if you are able to:

□ Solve nonlinear systems using the appropriate strategy

Also remember to

Review for Final Exam.

4𝑥 − 𝑦 = 1

1. Solve the following system of equations using your preferred method

−𝑦 + 𝑥 = 3

(𝑥 − 2)2 + (𝑦 + 3)2 = 4

You may bring your own questions for review next week.

MAC 1105 MATH GYM FALL 2021 Week 15

You may write your questions or topics to review with your LA here:

We wish you all the best on all your final exams. As you continue towards your degree,

remember all the study skills you learned in this course.