a) from the graph of f(x), for each value of x listed, choose the correct statement. i) x = -4 o f(x) is…

a) from the graph of f(x), for each value of x listed, choose the correct statement. i) x = -4 o f(x) is continuous at x = -4. o f(x) is not continuous at x = -4 because it is a removable discontinuity.

a) from the graph of f(x), for each value of x listed, choose the correct statement. i) x = -4 o f(x) is continuous at x = -4. o f(x) is not continuous at x = -4 because it is a removable discontinuity.

Answer

Explanation:

Step1: Recall continuity conditions

A function is continuous at a point if $\lim_{x\rightarrow a^{-}}f(x)=\lim_{x\rightarrow a^{+}}f(x)=f(a)$. At $x = - 4$, the function has a hole.

Step2: Identify discontinuity type

A removable discontinuity occurs when the limit of the function exists at a point but the function is not defined or has a different value at that point. Since the function has a hole at $x=-4$, the limit exists but the function value is not defined as - presented by the open - circle, so it's a removable discontinuity.

Answer:

$f(x)$ is not continuous at $x = - 4$ because it is a removable discontinuity.