In Mathematics / College | 2025-08-20

Consider the following function:

[tex]f(x)=\left\{\begin{array}{ll}
\frac{x^2-2 x-24}{x+4} & \text { if } x \neq-4 \\
-2 & \text { if } x=-4
\end{array}\right.[/tex]

Determine if [tex]f(x)[/tex] is continuous at [tex]x=-4[/tex]. If not, select the option with the correct reasoning as to why not.

A. Continuous at [tex]x=-4[/tex]
B. Not continuous at [tex]x=-4[/tex] because [tex]\lim _{x \rightarrow-4} f(x) \neq f(-4)[/tex]
C. Not continuous at [tex]x=-4[/tex] because [tex]\lim _{x \rightarrow-4} f(x)[/tex] does not exist
D. Not continuous at [tex]x=-4[/tex] because [tex]f(-4)[/tex] is undefined

Asked by jklmnop162