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Chapter 2: Q. 26 (page 124)

Find the average rate of change from 2to 3for each function f. Be sure to simplify.

f(x)=3x-4x2

Short Answer

Expert verified

The average rate of change is -17.

Step by step solution

01

Step 1. Find f(2) and f(3)

Consider the function f(x)=3x-4x2.

Now the function value for x=2is given as

role="math" localid="1645897024793" f(2)=3脳2-4脳22f(2)=6-4脳4f(2)=6-16f(2)=-10

Again, the function value for x=3is given as

role="math" localid="1645897053108" f(3)=3脳3-4脳32f(3)=9-4脳9f(3)=9-36f(3)=-27

02

Step 2. Find the average rate of change 

The average of change for the function f(x)from 2to 3is given as

f(3)-f(2)3-2=-27-(-10)1=-27+10=-17

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Most popular questions from this chapter

Exploration Graph y=x3. Then on the same screen graph y=(x-1)3+2. Could you have predicted the result?

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

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

Match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function

A right triangle has one vertex on the graph of y=9-x2,x>0, at x,y, another at the origin, and the third on the positive x-axis at x,0. Express the area Aof the triangle as a function of x.
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