complete parts (a) through (d) below. f(x)=7/(1 - 0.25x²) d={x|x≠2, - 2} (use a comma to separate answers as…

complete parts (a) through (d) below. f(x)=7/(1 - 0.25x²) d={x|x≠2, - 2} (use a comma to separate answers as needed.) (b) graph f. use the viewing window -20,20,4 by -20,20,4 (c) find any horizontal or vertical asymptotes. select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. the function has one vertical asymptote, (type an equation.) b. the function has two vertical asymptotes. the left - most asymptote is and the right - most asymptote is (type equations.) c. the function has no vertical asymptotes.

complete parts (a) through (d) below. f(x)=7/(1 - 0.25x²) d={x|x≠2, - 2} (use a comma to separate answers as needed.) (b) graph f. use the viewing window -20,20,4 by -20,20,4 (c) find any horizontal or vertical asymptotes. select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. the function has one vertical asymptote, (type an equation.) b. the function has two vertical asymptotes. the left - most asymptote is and the right - most asymptote is (type equations.) c. the function has no vertical asymptotes.

Answer

Explanation:

Step1: Find vertical asymptotes

Set the denominator equal to zero: $1 - 0.25x^{2}=0$. Then $0.25x^{2}=1$, $x^{2}=\frac{1}{0.25}=4$, so $x = 2$ or $x=- 2$.

Step2: Find horizontal asymptotes

Degree of numerator is $0$ and degree of denominator is $2$. As $x\to\pm\infty$, $y=\lim_{x\to\pm\infty}\frac{7}{1 - 0.25x^{2}} = 0$.

Answer:

(b) Without actually graph - ing software, we can't directly pick the graph. But we know the function has vertical asymptotes at $x = 2$ and $x=-2$ and a horizontal asymptote at $y = 0$. (c) B. The function has two vertical asymptotes. The left - most asymptote is $x=-2$ and the right - most asymptote is $x = 2$.