For the following exercises, consider the function shown in Figure 17. At what x-coordinates is the function discontinuous?

For the following exercises, consider the function shown in Figure 17.

At what x-coordinates is the function discontinuous?

Expert Solution

A function f (x) is continuous at x = a, only if it satisfies all the three following conditions:

• Condition 1: f (a) exists.

• Condition 2: limx→af(x) exists

• Condition 3: limx→af(x) = f(a)

Consider the graph provided in the textbook:

At x = -1, the limit does not exist, so the function is discontinuous at x = -1.

At x = 1, f(1) does not exist, so the function is discontinuous at x = 1.

At x = 2, the limit does not exist due to the vertical asymptote, so the function is discontinuous at x = 2.

So, the function is discontinuous at points x = -1, x = 1 and x = 2.

Junaid answered 1 year ago

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Question

For the following exercises, consider the function shown in Figure 17. At what x-coordinates is the function discontinuous?

Solutions

Expert Solution

Related Solutions

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