Question

Build a function whose domain is all real numbers other than -4, and whose range is all real numbers other than 5.

Answer 1

An example is the rational function
`y=(5x)/(x+4)`.

Explanation:

The graph of the rational function
`y=(5x)/(x+4)` has a vertical asymptote at x = -4 where the denominator is equal to zero. The function is undefined there, so the domain is all real numbers except -4.

The graph has a horizontal asymptote y = 5 so the domain is all real numbers except 5.

See the attached image for the graph of the function (purple) and it's vertical asymptote (black).