Question

What are the vertical and horizontal asymptotes for the function 3x^2/x^2-4

Answer 1

Answer: vertical asymptotes: x = 2, x = -2

              horizontal asyptote: y = 3

Step-by-step explanation:

$\dfrac{3x^2}{x^2-4}$

Vertical Asymptotes are the restrictions on "x", which is denoted by the denominator being unequal to zero.

x² - 4 = 0

(x + 2)(x - 2) = 0

x + 2 = 0      and       x - 2 = 0

     x = -2     and             x = -2

Horizontal Asymptotes are determined by the degree of the numerator (n) compared to the degree of the denominator (m) as follows:

• If n > m , then no horizontal asymptote (use long division to find slant asymptote)
• If n = m , then horizontal asymptote is coefficient of n divided by coefficient of m
• If n < m , then horizontal asymptote is: y = 0

In the given problem, the degree of both the numerator and denominator is 2 so horizontal asymptote is: $y = \dfrac{3}{1} = 3$

Answer 2

Answer:

d

Step-by-step explanation:

math