Question

1. what are the values of x where the graph of the rational function $f(x)=\frac{x+2}{x^{2}-x-12}$ is discontinuous?$x=-4$ and $x=3LXB0x=-2$ and $x=6$$x=-3$ and $x=4$

Explanation:

Step1: Identify denominator

Rational functions are discontinuous where their denominator equals 0. The denominator is $x^2 - x - 12$.

Step2: Set denominator to 0

$$x^2 - x - 12 = 0$$

Step3: Factor quadratic equation

Find two numbers that multiply to $-12$ and add to $-1$: $-4$ and $3$.
$$(x - 4)(x + 3) = 0$$

Step4: Solve for x

Set each factor equal to 0:
$x - 4 = 0 \implies x = 4$
$x + 3 = 0 \implies x = -3$

Answer:

D. $x = -3$ and $x = 4$