Question

question 6
2 pts
find all values of x where $\frac{x^{2}-9}{x - 3}$ is not continuous (enter
a\ if f is continuous for all values of x)

Explanation:

Step1: Recall continuity condition

A rational - function $\frac{f(x)}{g(x)}$ is discontinuous where $g(x)=0$.
For the function $y = \frac{x^{2}-9}{x - 3}$, the denominator is $g(x)=x - 3$.

Step2: Solve for the discontinuity

Set $x−3 = 0$.
$x-3=0$ implies $x = 3$.
We can simplify the function $\frac{x^{2}-9}{x - 3}=\frac{(x + 3)(x - 3)}{x - 3}=x + 3$ for $x
eq3$. But the original function is not defined at $x = 3$.

Answer:

$x = 3$