Question

graph all vertical and horizontal asymptotes of the rational function.
$f(x)=\frac{5}{-x^2 + 4}$

Explanation:

Step1: Find vertical asymptotes

Set denominator to 0: $-x^2 + 4 = 0$
Rearrange: $x^2 = 4$
Solve for $x$: $x = 2$ and $x = -2$

Step2: Find horizontal asymptote

Compare degrees of numerator/denominator:
Degree of numerator (0) < Degree of denominator (2)
Horizontal asymptote: $y = 0$

Answer:

Vertical asymptotes: $x=2$ and $x=-2$ (vertical dashed lines at these x-values)
Horizontal asymptote: $y=0$ (horizontal dashed line along the x-axis)