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Chapter 2: Q. 23 (page 113)

Write the function whose graph is the graph of y=x3, but is:

Reflected about the y-axis.

Short Answer

Expert verified

The function isy=-x3

Step by step solution

01

Step 1. Given information

The given function isy=x3

02

Step 2. Find the function for reflected about the y-axis.

For a function y=f(x), the reflection about the y-axis of the graph of the function is given by y=f(-x).

So substitute -xin place of xin the given function,

role="math" localid="1645860024694" y=(-x)3y=-x3

Therefore, the new function isy=-x3

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Most popular questions from this chapter

A right triangle has one vertex on the graph of y=9-x2,x>0, at x,y, another at the origin, and the third on the positive x-axis at x,0. Express the area Aof the triangle as a function of x.

True or False

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

Graph y=x. Then on the same screen graph y=2x, followed by y=4x, followed by

y=12x.What pattern do you observe? Can you predict the graph ofy=14x? ofy=5x

?

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.

g(x)=4x

Find the following for each function:

fx=3xx2-1

Part (a):f2

Part (b):f-2

Part (c):f-x

Part (d):-fx

Part (e):fx-2

Part (f):f2x
See all solutions

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