Question

Show all work to identify the asymptotes and zero of the function f of x equals 3 x over quantity x squared minus 9.

Answer 1

• Asymptotes: x = -3, x = 3, y = 0

Explanation:

Given function:

• f(x) = 3x / (x² - 9)

Zero of the function:

• f(x) = 0
• 3x / (x² - 9) = 0
• x = 0, x ≠ -3; 3

Vertical asymptotes:

• x² - 9 = 0
• x² = 9
• x = √9
• x = -3; x = 3

Horizontal asymptotes:

• The horizontal asymptote is y = 0, since the degree of the numerator is 1, while the degree of the denominator is 2.

The graph with asymptotes and zero is attached