Question

use the given graph of the function f to determine the type of discontinuity at each x - value.

1. what type of discontinuity does f have at x = - 4?
2. what type of discontinuity does f have at x = - 2?
3. what type of discontinuity does f have at x = 2?
4. what type of discontinuity does f have at x = 4?

choose one
removable
jump
infinite

Explanation:

Step1: Analyze $x = - 4$

As $x$ approaches - 4 from both sides, the function values go to positive or negative infinity. So it's an infinite discontinuity.

Step2: Analyze $x=-2$

The function has a hole at $x = - 2$. The limit exists as $x$ approaches - 2, but the function is not defined at that point. So it's a removable discontinuity.

Step3: Analyze $x = 2$

As $x$ approaches 2 from the left and right, the function approaches different finite - valued limits. So it's a jump discontinuity.

Step4: Analyze $x = 4$

The function has a hole at $x = 4$. The limit exists as $x$ approaches 4, but the function is not defined at that point. So it's a removable discontinuity.

Answer:

1. infinite
2. removable
3. jump
4. removable