Question

algebra 2 362403-6 fy - 1
benchmark test 2
due feb 5 - 11:
what are the horizontal and vertical asymptotes of the graph of $y = \frac{x - 10}{x^3 - 125}$ ?
a. $y = 10; x = 125$
b. $y = 10; x = 5$
c. $y = 0; x = 5$
d. $y = 0; x = 10$
question 27 of 30

Explanation:

Step1: Find vertical asymptote

Set denominator to 0:
$$x^3 - 125 = 0$$
Factor using difference of cubes:
$$(x-5)(x^2+5x+25)=0$$
Solve for $x$:
$x=5$ (quadratic has no real roots)

Step2: Find horizontal asymptote

Compare degrees: numerator degree = 1, denominator degree = 3. Since numerator degree < denominator degree, horizontal asymptote is $y=0$.

Answer:

C. $y = 0; x = 5$