Posted by **sam** on Tuesday, April 2, 2013 at 1:17pm.

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

-vertical asymptote with equation x=3

-horizontal asymptote with equation y=2

-hole at x=1

no x intercept

thank you

- advance functions gr12 -
**Steve**, Tuesday, April 2, 2013 at 1:49pm
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

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