BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.1, Problem 44E
To determine

To find: The values of f(3),f(0),f(2) and sketch the graph of piecewise function.

Expert Solution

Answer to Problem 44E

The value of f(3)=92 .

The value of f(0)=3 .

The value of f(2)=1 .

Explanation of Solution

Given:

The function is f(x)={312xif x<22x5if x2 .

Calculation:

Obtain the values of f(3),f(0) and f(2) as follows:

Since the value of x (=3) is less than 2, substitute −3 for x in the function f(x)=312x .

f(3)=312(3)=3+32=92

The value of f(3)=92 .

Since the value of x (=0) is less than 2, substitute 0 for x in the function f(x)=312x .

f(0)=312(0)=3

The value of f(0)=3 .

Since the value of x is equal to 2, substitute 2 for x in the function f(x)=2x5 .

f(2)=2(2)5=45=1

The value of f(2)=1 .

When x<2 , f(x)=312x is a line with slope 12 and y-intercept 3 that lies to the left of the line x = 2.

When x2 , f(x)=2x5 is a line with slope 2 and y-intercept −5 that lies to the right of the line x = 2.

The graph of f(x) is shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.1, Problem 44E

In Figure 1, the open dot indicates that the point (2, 2) is excluded and the closed dot indicates that the point (2, −1) is included.

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