   Chapter 9.2, Problem 1E Mathematical Applications for the ...

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

Solutions

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 xk for the function f(x) must exist.

The value of a function f(x) at the point k and the limit as xk 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=5 is;

f(5)=4

For the limit as x5 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?

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