Question

find all asymptotes, x - intercepts, and y - intercepts for the graph of the rational function and sketch the graph of the function.
f(x)=\frac{-1}{(x + 3)^2}
find all vertical asymptotes. select the correct choice below and, if necessary, fill in the answer box within your choice.
a. (x=-3) (simplify your answer. use a comma to separate answers as needed.)
b. there are no vertical asymptotes.
find the horizontal or oblique asymptote. select the correct choice below and, if necessary, fill in the answer box within your choice.
a. (y=)
(simplify your answer.)
b. there is no horizontal nor oblique asymptote.

Explanation:

Step1: Find vertical asymptote

Set denominator equal to 0. $(x + 3)^2=0$, so $x=-3$.

Step2: Find horizontal asymptote

Degree of numerator is 0 and degree of denominator is 2. Since degree of numerator < degree of denominator, $y = 0$.

Step3: Find x - intercept

Set $y = 0$. $\frac{-1}{(x + 3)^2}=0$, no solution as numerator is - 1, so no x - intercepts.

Step4: Find y - intercept

Set $x = 0$. $y=\frac{-1}{(0 + 3)^2}=-\frac{1}{9}$.

Answer:

Vertical asymptote: $x=-3$
Horizontal asymptote: $y = 0$
x - intercept: None
y - intercept: $y=-\frac{1}{9}$