write an equation for a rational function whose graph has all of the indicated features:

Question

-vertical asymptote with equation x=3
-horizontal asymptote with equation y=2
-hole at x=1
no x intercept

thank you

Answer 1

vertical asymptote needs 1/(x-3)
horizontal asymptote needs equal degree, top/bottom = 2
hole needs (x-1) top and bottom

So, so far we have

2(x-1)/((x-1)(x-3))

but that has hor asymp y=0, so we need equal degree top and bottom

2(x-1)(x+1)/(x-1)(x-3)

but that also has x-intercept. So, let's square it:

y = 1+((x^2-1)/(x^2-4x+3))^2