Consider the function

Question

 Consider the function

f(x)= (8x−4)/(−4x−9)(3x−4)

Enter the equations of the vertical asymptotes. If there are no vertical asymptotes, enter none. If there is more than one vertical asymptote, enter a list of the equations separated by a comma (e.g., x=20, x=-7).

Vertical asymptotes =

Enter the equations of the horizontal asymptotes. If there are no horizontal asymptotes, enter none. If there is more than one horizontal asymptote, enter a list of the equations separated by a comma (e.g., y=20, y=-7).

Horizontal asymptotes: =

Answer 1

Hi Rachel K.

Anything that would result in division by zero is a vertical Asymptote, so in your denominator

(-4x - 9)(3x - 4)

x≠ -2.25

x≠ 4/3

That means there will be boundaries at x = -2.25 and x=4/3

For horizontal Asymptotes you need to determine if the exponent in the denominator is larger than the exponent in the numerator. You can check into the requirements for horizontal Asymptotes in your text or online.

You can also let me know which spelling is correct I've seen Asymptotes and Asymptope