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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

True or False The independent variable is sometimes

referred to as the argument of the function.

In Problems 33鈥� 44, determine algebraically whether each function is even, odd, or neither.
h(x)=xx2-1

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.

hx=x+1

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

Test the equation y=5x2-1for symmetry with respect to the x-axis, the y-axis, and the origin.
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