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Chapter 2: Q. 104 (page 116)

Reflection about the x-axis Open the reflection about the xaxis 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 the graphf(x)=g(x)

Step by step solution

01

Given information

Given the reflection about yaxis

02

Checking the translation

Assume that g(x)=f(ax)

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 y-axis, therefore g(x)=f(-x)is the reflection of the graphg(x)=f(x)

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Most popular questions from this chapter

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)

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.

f(x)=x-13+2

If 4,2is a point on the graph of y=f(x), which of the following points must be on the graph of y=f2(x)?

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 Problems 19-26,write the function whose graph is the graph of y=x3but is:

Shifted to the right4 units
See all solutions

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