Question

graph all vertical and horizontal asymptotes of the rational function.
$f(x)=\frac{9}{-x+4}$

Explanation:

Step1: Find vertical asymptote

Set denominator to 0: $-x + 4 = 0 \Rightarrow x = 4$

Step2: Find horizontal asymptote

Degrees of numerator/denominator equal (0=1? No: numerator degree 0, denominator degree 1 → HA is $y=0$)

Step3: Graph asymptotes

Draw vertical line $x=4$ and horizontal line $y=0$ (x-axis) on the grid.

Answer:

Vertical asymptote: $x=4$; Horizontal asymptote: $y=0$
(Graph: Vertical line through (4,0), horizontal line along x-axis)