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Chapter 2: Q. 19 (page 113)

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

Shifted to the right4 units

Short Answer

Expert verified

The function isy=(x-4)3.

Step by step solution

01

Step 1. Given Information 

It is given that the function whose graph is the graph of y=x3but it is shifted to the right by4 units.

02

Step 2. Stating the function of the graph

If the argument xof a function f is replaced by x-h,h>0,the graph of the new function y=f(x-h) is the graph of fshifted horizontally right hunits.

Since the graph is shifted to the right by4 units, the function of the graph isy=(x-4)3.

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Most popular questions from this chapter

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

Shifted to the left 4units

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.

h(x)=12x

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

A rectangle is inscribed in a semicircle of radius 2. See the figure. Let P=x,ybe the point in quadrant I that is vertex of the rectangle and is on the circle.

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

Part (b): Express the perimeter pof the rectangle as a function of x.

Part (c): Graph A=Ax. For what value of xis Alargest?

Part (d): Graph p=px. For what value of xis plargest?

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
See all solutions

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