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Chapter 2: Q. 103 (page 103)

Reflection about the y-axis Open the reflection about the yaxis applet. Move your mouse to grab the slider and change the value of afrom 1 to-1

Short Answer

Expert verified

The function is the reflection of graphg(x)=f(x)

Step by step solution

01

Given information

Given the reflection about yaxis

02

Checking the transformation

Assume that g(x)=af(x)

If the values of achanges from 1to -1, then g(x)=-f(x)

Since y=f(x)and

y=-f(x)are equidistance from the x-axis, therefore g(x)=-f(x)is the reflection of the graph g(x)=f(x)

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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

A rectangle has one corner in quadrant I on the graph of y=16-x2, another at the origin, a third on the positive y-axis and the fourth on the positive x-axis. See the figure.

Part (a): Express the area Aof the rectangle as a function of x.

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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.

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

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