Question

f(x) = \frac{-7}{x + 1}
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.
your answer

Explanation:

Step1: Find vertical asymptote

Set denominator to 0: $x+1=0 \implies x=-1$

Step2: Find horizontal asymptote

For rational function $\frac{a}{bx+c}$, horizontal asymptote is $y=0$

Step3: Find points for $x < -1$

Choose $x=-2$: $f(-2)=\frac{-7}{-2+1}=7$, so point $(-2,7)$
Choose $x=-8$: $f(-8)=\frac{-7}{-8+1}=1$, so point $(-8,1)$

Step4: Find points for $x > -1$

Choose $x=0$: $f(0)=\frac{-7}{0+1}=-7$, so point $(0,-7)$
Choose $x=6$: $f(6)=\frac{-7}{6+1}=-1$, so point $(6,-1)$

Answer:

Vertical asymptote: $x=-1$ (dashed line)
Horizontal asymptote: $y=0$ (dashed line)
Points on left of asymptote: $(-2,7)$, $(-8,1)$
Points on right of asymptote: $(0,-7)$, $(6,-1)$
(Graph by plotting the dashed asymptotes, the four points, then drawing the two branches of the hyperbola approaching the asymptotes)