Question

write a rational function r(x) which is vertical asymptotes at x=-2, a removable discontinuity at x=4 and a zero at x =5 THANKS SO MUCH

Answer 1

you want a vertical asymptote at \(x=-2\) so put a \(x+2\) in the denominator

Answer 2

you want a "removable discontinuity" at \(x=4\) so put a \(x-4\) in the denominator, and also make sure the numerator has a factor of \(x-4\) as well

Answer 3

so far we have
\[\frac{x-4}{(x+2)(x-4)}\]
now one more thing
you want a zero at \(x=5\) so put a factor of \(x-5\) in the numerator

Answer 4

you can use as an answer
\[r(x)=\frac{(x-5)(x-4)}{(x+2)(x-4)}\]

Answer 5

if you like you can multiply that out top and bottom to write it not in factored form