HW collaga algabra

Homework, Week #3 – over Lessons 4, 5 and 6, and Workshop 3 Due at the start of class 9/12/14 Name: ______________________

As you do these problems, show your work clearly!

#1. Explain clearly whether or not the following relation is a function, and why.

NumberOfFloors[“building on the WSU campus”]

#2. Consider the function SolutionSet(“single-variable equation”). Now, an input is given for this function; use algebra to find the associated output and write it using set notation.

SolutionSet(

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4x3 − 36x = 0 ) = __________

#3. Some input-output pairs of a non-arbitrary function are given.

???(Thanksgiving) = November, ???(Memorial Day) = June, ???(Valentine’s Day) = February, ???(Labor Day) = September

a) Try to figure out the rule-of-correspondence for it; then write it using Descriptive Function Notation.

b) Write a sentence to describe the domain of this function.

#4. Given the function PurchasePrice(“Monopoly property”), match the four terms below with the appropriate descriptions. A. a purchase price of a Monopoly property C. the set of all Monopoly properties B. a Monopoly property D. the set of all purchase prices of Monopoly properties

a) Domain b) Range c) Input d) Output

#5. Consider the arithmetic function DivideTenByTheInputNumber(“number”). Use it to do the following:

a) Write down the output if the input is chosen to be x.

DivideTenByTheInputNumber(

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x ) = ________

b) Represent the function above using Function Notation, with input variable x and function variable g.

#6. A line passes through the points

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−3,−2( ) and

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9,−7( ) . What is the slope of a line that is perpendicular to this one? Circle your answer.

#7. Find all points on the y-axis

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0, y( ) such that the distance between them and the point

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3,−4( ) is

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d = 5.

#8. Let h be the function defined by

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h x( ) = 4x

5x +1 . Find the output values of the function, given the input values below (and simplify them). Write your input-output answers as equations; if you are not sure what this means, ask your teacher! Circle your answers. Note that the first problem is done for you, with the answer circled!

a)

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h 1( ) b)

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h −3( ) c)

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h 1 5      

h(1) =4 6

2 3

=

h(1) = 2 3

#9. Imagine that we are told that function f is algebraic, and that if the number 11 is supplied to it as an input, the corresponding output value of the function is 25. Now, write an equation using Function Notation to capture this input-output pair. (If you are not sure what this means, ask your teacher!) Hint: your answer should be of the same form as your answers to problem #8 above.

#10. For the function below, determine its implied domain. Write your answer using interval notation. (You may wish to review interval notation, which was explained in Lesson 2.) Circle your answer.

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r x( ) = x 2 −9

x 2 −7x +6