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Chapter 2: Q. 20 (page 124)

Determine(algebraically)whethere the given function is even, odd,or neither.

G(x)=1-x+x2

Short Answer

Expert verified

The given functionG(x)=1-x+x2is neither even nor odd.

Step by step solution

01

Step 1.Given information

The given function G(x)=1-x+x2

02

Step 2. Determine the given function is even,odd or neither

The function is even if G(-x)=G(x)and odd if G(-x)=-G(x).If none of these conditions are satisfied.

Find G(-x) by replacing -x forx in the given function.
G(-x)=1-(-x)+(-x)3=1+x-x3

We can see that G(-x)鈮�G(x)andG(-x)鈮�-G(x).Therefore the given function is neither even nor odd

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Most popular questions from this chapter

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

The set of all images of the elements in the domain of a function is called the _________.

In March 2011, Peoples Energy had the following rate schedule for natural gas usage in single- family residences:

Monthly service charge- \(18.95

Per therm service charge

1st50therms- \)0.33372/therm

Over 50therms- \(0.12360/therm

Gas charge- \)0.5038/therm

(a) What is the charge for using 50therms in a month?

(b) What is the charge for using 500therms in a month?

(c) Develop a model that relates the monthly charge Cfor xtherms of gas.

(d) Graph the function found in part (c)

match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

fx=-x3
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