Question

# Which function has a graph with a vertical asymptote at x = 3? Select all that apply .

- Non of the above

## The correct answer is:

### a) The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

x^{2} + 2x - 15= 0

x^{2} + 5x -3x - 15= 0

x(x + 5) – 3(x + 5)

(x + 5) (x - 3)

x = -5 and x = 3

The vertical asymptote of the rational function is x =-5 and x =3

b) The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

x^{2} + 7x + 12= 0

x^{2} + 4x + 3x + 12= 0

x(x + 4) + 3(x + 4)

(x + 4)(x + 3)

x = -4 and x = -3

The vertical asymptote of the rational function is x =-4 and x = -3.

c) The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

x + 9 = 0

x = -9

Function

a. has vertical asymptote at x = 3.

^{2}+ 2x - 15= 0

x

^{2}+ 5x -3x - 15= 0

x(x + 5) – 3(x + 5)

(x + 5) (x - 3)

x = -5 and x = 3

The vertical asymptote of the rational function is x =-5 and x =3

b) The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

^{2}+ 7x + 12= 0

x

^{2}+ 4x + 3x + 12= 0

x(x + 4) + 3(x + 4)

(x + 4)(x + 3)

x = -4 and x = -3

The vertical asymptote of the rational function is x =-4 and x = -3.

c) The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

x = -9

Function

a. has vertical asymptote at x = 3.