advance functions gr12

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

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  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

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