math homework

In this discussion, you will be assigned two equations with which you will then do a variety of math work having to do with mathematical functions. Read the following instructions in order and view the example to complete this discussion:

· Find your two equations in the list below based on the last letter of your last name.

If the last letter of your last name is	On pages 708 – 711, solve the following problems
A or B	22 and 30
C or D	24 and 32
E or F	26 and 34
G or H	28 and 36
I or J	12 and 46
K or L	14 and 48
M or N	16 and 50
O or P	18 and 52
Q or R	20 and 54
S or T	2 and 56
U or V	4 and 58
W or X	6 and 60
Y or Z	8 and 64

· There are many ways to go about solving math problems. For this assignment you will be required to do some work that will not be included in the discussion. First, you need to graph your functions so you can clearly describe the graphs in your discussion. Your graph itself is not required in your post, although the discussion of the graph is required. Make sure you have at least five points for each equation to graph. Show all math work for finding the points.

· Specifically mention any key points on the graphs, including intercepts, vertex, or start/end points.  (Points with decimal values need not be listed, as they might be found in a square root function. Stick to integer value points.)

· Discuss the general shape and location of each of your graphs.

· State the domain and range for each of your equations. Write them in interval notation.

· State whether each of the equations is a function or not giving your reasons for the answer.

· Select one of your graphs and assume it has been shifted three units upward and four units to the left. Discuss how this transformation affects the equation by rewriting the equation to incorporate those numbers.

· Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.):

· Function

· Relation

· Vertical Line test

· Transformation

Your initial post should be at least 250 words in length. Support your claims with examples from required material(s) and/or other scholarly resources, and properly cite any references. Respond to at least two of your classmates’ posts by Day 7.

Absolute value functions

Problem #20

y = | x − 1 | + 2

Graph each relation, and state its domain and range.

problem #54

Example for problem 54

8

Graphing relations that are not functions

Graph each relation, and state the domain and range.

a)	x = y2
b)	x = | y − 3 |

Solution

a)	Because the equation x = y2 expresses x in terms of y, it is easier to choose the y-coordinate first and then find the x-coordinate: Figure 11.16 shows the graph. The domain is [0, ∞) and the range is (−∞, ∞). Figure 11.16
b)	Again we select values for y first and find the corresponding x-coordinates: Plot these points as shown in Fig. 11.17. The domain is [0, ∞) and the range is (−∞, ∞).

Figure 11.17

Now do Exercises 45–56

Note that y = x2 is a function and x = y2 is not a function because we have agreed that x is always the independent variable and y the dependent variable. You can determine the y-coordinate from x in y = x2, but y can't be determined from x in x = y2.If we use variables other than x and y, then we must know which is the independent variable to decide if the equation is a function. For example, if W = a2 and a is the independent variable, then W is a function of a.