advance functions gr12
posted by sam .
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

vertical asymptote needs 1/(x3)
horizontal asymptote needs equal degree, top/bottom = 2
hole needs (x1) top and bottom
So, so far we have
2(x1)/((x1)(x3))
but that has hor asymp y=0, so we need equal degree top and bottom
2(x1)(x+1)/(x1)(x3)
but that also has xintercept. So, let's square it:
y = 1+((x^21)/(x^24x+3))^2