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Question

Removable discontinuity at x=-5 Jump discontinuity at x=1
Step-by-step explanation:
In the graphs shown, the hole exist in the function at x=-5. These holes are called removable discontinuities.
Hence, one type of discontinuity exists is removable discontinuity at x=-5
The function gives different values at x=1. When this happens, we say the function has a jump discontinuity.
Jump Discontinuities exist where both one-sided limits exist, but have different values. Hence, at x=1 jump discontinuity exists.

Answer 1

The function exhibits a removable discontinuity at x=-5 and a jump discontinuity at x=1. The removable discontinuity occurs when the graph has a hole at x=-5, while the jump discontinuity occurs when the function has different values at x=1.