Question

graph all vertical and horizontal asymptotes of the rational function. f(x)=\frac{10}{-2x - 7}

Explanation:

Step1: Find vertical asymptote

Set denominator to 0: $-2x -7 =0 \Rightarrow x=-\frac{7}{2}=-3.5$

Step2: Find horizontal asymptote

Degrees of numerator/denominator equal (0/1? No: numerator degree 0, denominator degree1 → limit to 0): $\lim_{x\to\pm\infty}\frac{10}{-2x-7}=0 \Rightarrow y=0$

Answer:

Vertical asymptote: $x=-3.5$ (dashed vertical line at $x=-3.5$); Horizontal asymptote: $y=0$ (x-axis, dashed or solid as required)