Question

graph the rational function.
$f(x)=\frac{6}{-x + 6}$
start by drawing the vertical and horizontal asymptotes. then plot two points on each piece of the graph. finally, click on the graph - a - function button.

Explanation:

Step1: Find vertical asymptote

Set denominator to 0: $-x + 6 = 0$
Solve for $x$: $x = 6$

Step2: Find horizontal asymptote

Compare degrees: numerator degree 0, denominator degree 1.
Horizontal asymptote: $y = 0$

Step3: Plot left asymptote points

Choose $x=0$: $f(0)=\frac{6}{-0+6}=1$ → Point $(0,1)$
Choose $x=3$: $f(3)=\frac{6}{-3+6}=2$ → Point $(3,2)$

Step4: Plot right asymptote points

Choose $x=7$: $f(7)=\frac{6}{-7+6}=-6$ → Point $(7,-6)$
Choose $x=9$: $f(9)=\frac{6}{-9+6}=-2$ → Point $(9,-2)$

Answer:

1. Draw vertical asymptote $x=6$ (dashed vertical line)
2. Draw horizontal asymptote $y=0$ (dashed horizontal line)
3. Plot points $(0,1)$, $(3,2)$ on the left of $x=6$, and $(7,-6)$, $(9,-2)$ on the right of $x=6$
4. Draw two curves: one passing through the left points approaching both asymptotes, and one passing through the right points approaching both asymptotes