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Chapter 2: Q. 27 (page 113)

Find the function that is finally graphed after each of the following transformations is applied to the graph of y=xin the order stated.

(1) Shift up 2units

(2) Reflect about the x-axis

(3) Reflect about the y-axis

Short Answer

Expert verified

The function after all the transformation isy=--x+2

Step by step solution

01

Step 1. Given information

We have been given functiony=x

02

Step 2. Use the first transformation

If the graph of y=f(x)is shifted up by 2units then add 2to f(x).

So,

y=x+2

03

Step 3. Use the second transformation

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

So,

y=-x+2

04

Step 4. Use the third transformation 

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,

y=--x+2

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Most popular questions from this chapter

True or False If no domain is specified for a function f, then the domain of fis taken to be the set of real numbers.

If f(x)=-3xifx<-10ifx=-12x2+1ifx>-1

Find: (a)f(-2) and (b) f(-1) (c)f(0)

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)=x3-1

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

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)=x3+1
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