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Chapter 2: Q. 9 (page 112)

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 functionH.y=-x+2.

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 

When the right side of the function y=f(x)is multiplied by -1the graph of the new function y=-f(x) is the reflection about the x-axis of the graph of the function role="math" localid="1645858147911" y=f(x).

Thus, the function whose graph is the reflection of the graph of y=x in the x-axis is y=-x.

03

Step 3. Stating the function of the graph

If the argument x of a function f is replaced by x+h,h>0,the graph of the

new function y=f(x+h) is the graph of f shifted horizontally left hunits.

Since the graph ofy=-x is shifted horizontally left by 2units

The function of the given graph isy=-x+2.

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Most popular questions from this chapter

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

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

Part (a): Express the area Aof 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 ofxis p largest?

In Problems 33鈥� 44, determine algebraically whether each function is even, odd, or neither.

F(x)=2xx

In March 2011, Nicor Gas had the following rate schedule for natural gas usage in single-family residences:

Monthly customer charge -\(13.55

Distribution charge

First 20therms-0.1473/therm

Next 30therm -\)0.0579/therm

Over 50therm -\(0.0519/therm

Gas supply charge-\)0.51/therm

(a) What is the charge for using 40therms in a month?

(b) What is the charge for using 150therms in a month?

(c) Develop a model that gives the monthly charge Cfor x therms of gas.

(d) Graph the function found in part (c).

The interval (2, 5) can be written as the inequality ___________
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