list all the asymptotes of the following function, then graph the function. f(x)=3x/(x² - 25) choose the…

list all the asymptotes of the following function, then graph the function. f(x)=3x/(x² - 25) choose the correct asymptotes below a. x = 5, x = - 5 b. x = 3, x = - 3, y = 0 c. x = 5, x = - 5, y = 0 d. x = 3, x = - 3 choose the correct graph below
Answer
Explanation:
Step1: Find vertical asymptotes
Set denominator equal to 0. Given $f(x)=\frac{3x}{x^{2}-25}$, and $x^{2}-25=(x + 5)(x - 5)$. So $(x + 5)(x - 5)=0$, then $x=5$ or $x=-5$.
Step2: Find horizontal asymptote
Degree of numerator $n = 1$ and degree of denominator $m=2$. Since $n<m$, the horizontal - asymptote is $y = 0$.
Answer:
C. $x = 5,x=-5,y = 0$