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Chapter 2: Q. 4 (page 112)

True or False

The graph of y=-f(x)is the reflection about the x-axis of the graph of y=f(x).

Short Answer

Expert verified

True

Step by step solution

01

Step 1. Concept Used

When the right side of the function y=f(x)is multiplied by -1, the graph of the new function y=-f(x)is the reflection about the x-axis of the graph of the function y=f(x).

02

Step 2. Identify true or false

As -1is multiplied to the right hand side of the function y=f(x)to get the function y=-f(x).

So the two functions are reflections of each other about the x-axis.

So the statement given is true.

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Most popular questions from this chapter

In Problems 7–18, 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

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)

The function f(x)=x2 is decreasing on the interval _____.

Exploration Graph y=x3,y=x5, and y=x7 on the same screen. What do you notice is the same about each graph? What do you notice that is different?

Exploration Graph y=x. Then on the same screen graph y=-x. What pattern do you observe? Now try y=2x+1 and y=2(-x)+1. What do you conclude?
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