Chapter 9.2, Problem 1E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# In Problems 1 and 2, refer to the figure. For each given x-value, use the figure to determine whether the function is continuous or discontinuous at that x-value. If the function is discontinuous, state which of the three conditions that define continuity is not satisfied.(a) x = − 5 (b) x = 1 (c) x = 3 (d) x = 0

(a)

To determine

Whether the function y=f(x) is continuous or discontinuous and the conditions used to reach the inference from the figure when the point of evaluation is x=5.

Explanation

Given Information:

The graph is given as

Explanation:

For a function f(x) to be continuous at a point k, it must satisfy the following conditions:

The value of a function f(x) at the point k must exist.

The limit as xâ†’k for the function f(x) must exist.

The value of a function f(x) at the point k and the limit as xâ†’k for the function f(x) must be equal.

The graph is given as;

From the graph, the value of the function f(x) at x=âˆ’5 is;

f(âˆ’5)=4

For the limit as xâ†’âˆ’5 to exist, the left-side limit must be equal to the right-hand limit

(b)

To determine

Whether function y=f(x) is continuous or discontinuous and the conditions used to reach the inference from the figure when the point of evaluation is x=1.

(c)

To determine

Whether function y=f(x) is continuous or discontinuous and the conditions used to reach the inference from the figure when the point of evaluation is x=3.

(d)

To determine

Whether function y=f(x) is continuous or discontinuous and the conditions used to reach the inference from the figure when the point of evaluation is x=0.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started