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Chapter 2: Q. 18 (page 113)

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

Short Answer

Expert verified

The given graph is matched to the functionK.y=2x.

Step by step solution

01

Step 1. Given Information 

There is the given graph we have to match each graph to its functions.

02

Step 2. Identifying the function of the graph 

The given graph is similar to the function of the graph y=xbut it is vertically stretched by a factor of 2.

When the right side of a function y=f(x) is multiplied by a positive number a, the graph of the new function y=af(x) is obtained by multiplying each y-coordinate on the graph of y=f(x) by a. The new graph is a vertically stretched (ifa>1)version of the graph of y=f(x).

Since the given graph is vertically stretched by factor of 2.

The function of the given graph isrole="math" localid="1645865928495" y=2xthat matched to option K.

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Most popular questions from this chapter

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)=x2-1

True or FalseThe cube root function is odd and is decreasing on the interval (-鈭�,鈭�).

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Part (a): Express the total area Aenclosed by the pieces of wire as a function of the length x of a side of the square.

Part (b): What is the domain of A?

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A wire 10meters long is to be cut into two pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle.

Part (a): Express the total area Aenclosed by the pieces of wire as a function of the length x of a side of the equilateral triangle.

Part (b): What is the domain of A?

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

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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