find the vertical and horizontal asymptotes of f and the graph of f that includes the asymptotes…

find the vertical and horizontal asymptotes of f and the graph of f that includes the asymptotes. f(x)=7x/(x² - 16) choose the correct asymptotes. a. x = 7, x = - 7, y = 0 b. x = 4, x = - 4, y = 0 c. x = 4, x = - 4 d. x = 7, x = - 7

find the vertical and horizontal asymptotes of f and the graph of f that includes the asymptotes. f(x)=7x/(x² - 16) choose the correct asymptotes. a. x = 7, x = - 7, y = 0 b. x = 4, x = - 4, y = 0 c. x = 4, x = - 4 d. x = 7, x = - 7

Answer

Explanation:

Step1: Find vertical asymptotes

Set the denominator equal to 0. Given $f(x)=\frac{7x}{x^{2}-16}$, and $x^{2}-16=(x + 4)(x - 4)$. So $(x + 4)(x - 4)=0$. Solving for $x$, we get $x=4$ or $x=-4$.

Step2: Find horizontal asymptotes

Since the degree of the numerator ($n = 1$) is less than the degree of the denominator ($m=2$), the horizontal - asymptote is $y = 0$.

Answer:

B. $x = 4,x=-4,y = 0$