Help with rational functions

[eli2099]

I got this as a HW question

Write an equation of a rational function with the properties
*x-intercept at 5
*y-intercept at -5/8
*vertical asymptote with equation x=-8/3
*horizontal asymptote with equation y=1/3

someone help please and thank you!

 

[Dr.Peterson]

Write an equation of a rational function with the properties
*x-intercept at 5
*y-intercept at -5/8
*vertical asymptote with equation x=-8/3
*horizontal asymptote with equation y=1/3

Build up the function piece by piece:

• What does it tell you about the numerator, that there is an x-intercept at 5?
• What does it tell you about the whole function that there is a y-intercept at -5/8? (I'd leave this fact for last, after the other pieces are filled in.)
• What does it tell you about the denominator, that there is a vertical asymptote x=-8/3?
• What does it tell you about the whole function that there is a horizontal asymptote y=1/3?

(You'll find that at least one requirement will occur naturally when the rest are taken care of.)

Please show work, so we can see what additional help you need.