Question

Identify the Vertical and Horizontal Asymptotes for the following functions:

f(x) = 2/(x - 1) + 4

O f(x) has a vertical asymptote at x = 4 and a horizontal asymptote at y = 1
O f(x) has a vertical asymptote at x = 1 and a horizontal asymptote at y = -4
O f(x) has a vertical asymptote at x = 1, but no horizontal asymptote
O f(x) has a vertical asymptote at x = 1 and a horizontal asymptote at y = 4

Answer 1

The function f(x) = 2/(x - 1) + 4 has a vertical asymptote at x = 1 and a horizontal asymptote at y = 4.

Step-by-step explanation:

The function f(x) = 2/(x - 1) + 4 has a vertical asymptote at x = 1 and a horizontal asymptote at y = 4.

To find the vertical asymptote, we set the denominator equal to zero and solve for x. In this case, x = 1 is the value that makes the denominator zero.

To find the horizontal asymptote, we look at the degree of the numerator and denominator. Since the degree of the numerator is less than the degree of the denominator by one, the horizontal asymptote is y = 0, which simplifies to y = 4 when we account for the vertical shift of 4.