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Chapter 2: Q. 64 (page 91)

Find the average rate of change of hx=x2-2x+3

(a) From-1to1

(b) From 0to 2

(c) From2to5

Short Answer

Expert verified

(a) The average rate of change is-1.

(b) The average rate of change is0.

(c) The average rate of change is5.

Step by step solution

01

Step 1. Given information.

We have:

hx=x2-2x+3

02

Part a. Step 1. Find the average rate of change from -1 to 1.

The function is hx=x2-2x+3.

Average rate of change is given by:

localid="1646220271324" 鈭�y鈭�x=f(b)-f(a)b-a

Here, a=-1,b=1:

localid="1646220297606" 鈭�y鈭�x=f(1)-f(-1)1--1=12-2(1)+1--12-2(-1)+11+1=-2

03

Part b. Step 1. Find the average rate of change from 0 to 2.

The function is hx=x2-2x+3.

Average rate of change is given by:

鈭�y鈭�x=f(b)-f(a)b-a

Here, a=0,b=2:

role="math" localid="1646220402827" 鈭�y鈭�x=f(2)-f(0)2-0=22-2(2)+1-02-2(0)+12=0

04

Part c. Step 1. Find the average rate of change from 2 to 5.

The function is hx=x2-2x+3.

Average rate of change is given by:

鈭�y鈭�x=f(b)-f(a)b-a

Here, a=2,b=5:

鈭�y鈭�x=f(5)-f(2)5-2=52-2(5)+1-22-2(2)+13=5

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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.

hx=x+1

When functions are defined by more than one equation, they are called __________________ functions.

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)=2x3

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

The set of all images of the elements in the domain of a function is called the _________.
See all solutions

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