Answer
common factor $x+1$
x-intercept=3
y-intercept=9
no asymptotes.
domain: $(-\infty,-1)\cup(-1,\infty)$
range: $[0,\infty)$
Work Step by Step
1. Use synthetic division as shown in the figure, we can factorize the numerator as
$(x+1)(x^2-6+9)=(x+1)(x-3)^2$, thus we can identify that $x+1$ is a common factor
of the numerator and the denominator, and a hole is at $(-1,16)$
2. We can identify the following from the function:
Let $y=0$, we get x-intercept=3
Let $x=0$, we get y-intercept=9
There are no asymptotes.
3. The graph of the rational function is shown in the figure and we can find
domain: $(-\infty,-1)\cup(-1,\infty)$
range: $[0,\infty)$
