Question

Please help!!! Thanks!!!

Find an equation with the given properties. It must be rational and cannot be a polynomial.
Horizontal asymptote at y=4
Vertical asymptote at x=2
Hole at x=3

Answer 1

what does a hole mean?

Answer 2

it is a piece of the graph that does not have a value at that spot

Answer 3

a whole is a point of discontinuity... this is where there is a common factor in the numerator and denominator...

so looking at the denominator you need

zeros x = 2 and x = 3 so the binomial factors are (x -2)(x -3)

for a horizontal asymptote of y = 4 you need the degree of the numerator to be the same as the degree of the denominator and 4 times larger. you also need (x -3) in the numerator.

so you need a linear factor in the numerator

it looks like

\[y = \frac{4(x -3)(your ~linear ~factor)}{(x -3)(x -2)}\]

hope it helps