RogaCalcET2 2.4.004.Tutorial.SA.

 
Problem Statement

Consider the graph of a function g.

Find the point c at which the function has a jump discontinuity but is left-continuous. What value should be assigned to g(c) to make g right-continuous at x = c?

 
Step 1

A function g has a jump discontinuity at x = c if and exist, but are not equal.

Question Sequence

Question 1

The graph of g has jump discontinuites at x = and x = 5.

Incorrect.
Correct.

 
Step 2

A function g is left-continuous at x = c if .

Question Sequence

Since the problem asks for a point on the graph that is both a jump discontinuity and is left-continuous, check x = 1 and x = 5 to determine if the function is left-continuous at either of these values.

Question 3

For x = 1: = and g(1) = .

For x = 5: = and g(5) = .

Correct.
Incorrect.

 
Step 3

A function g is right-continuous at x = c if .

Question 5

Since = , to redefine the given function g to make it right-continuous at x = 1, assign g(1) = .

Correct.
Incorrect.