Question

1. graph the function: (f(x)=\frac{x^{2}-5}{x + 2}). state whether the function is continuous at (x=-2). if the function is discontinuous, then state whether the discontinuity is removable or non - removable.

Explanation:

Step1: Check function value at x=-2

The function $f(x)=\frac{x^{2}-5}{x + 2}$ is undefined at $x=-2$ since denominator is 0.

Step2: Find the limit as x approaches -2

$\lim_{x
ightarrow - 2}\frac{x^{2}-5}{x + 2}=\frac{(-2)^{2}-5}{-2 + 2}=\frac{4 - 5}{0}$, limit does not exist.

Step3: Determine discontinuity type

Since limit does not exist at $x=-2$, it is a non - removable discontinuity.

Answer:

The function is discontinuous at $x=-2$ and the discontinuity is non - removable.