Question

Describe the continuity of the graphed function. Select all that apply.

Answer 1

Using continuity concepts, it is found that the correct options are:

• The function is continuous at x = -4.
• The function has an infinite discontinuity at x = -1.

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A function f(x) is continuous at x = a if:

$\lim_{x \rightarrow a^{-}} f(x) = \lim_{x \rightarrow a^{+}} f(x) = f(a)$

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• At x = -4, there are no changes in the definition of the function, thus, it is continuous.
• At x = -1, we have that:

$\lim_{x \rightarrow -1^-} f(x) = 0$

$\lim_{x \rightarrow -1^+} f(x) = f(1) = 1$

• A different definition depending on the which side of -1 the function is, thus, it is a jump discontinuity.

A similar problem is given at brainly.com/question/21447009