Equation for a rational function

Question

find the equation for a rational function that has a zero at x=2 a hole at x=7 and asymptotes at x=5 and y=4

 

 

I am just confused on the horizontal asymptote I know that there is a horizontal asymptote at y=4 but I am confused as to how this is represented in the equation 

 

 

thank you!

Answer 1

 

y = 4(x-2)(x-7)/(x-5)(x-7) = (4x²-36x+64)/(x²-12x+35)

 

• The 4 in the numerator is the horizontal asymptote at y=4
• The (x-2) in the numerator creates the zero at x=2
• The (x-7) in the denominator normally creates a vertical asymptote at x=7.  However, it cancels with the (x-7) in the numerator, creating a hole instead of an asymptote
• The (x-5) in the denominator creates the vertical asymptote at x=5