Question

Identify the discontinuities, graph, and find the zeros of each rational function.

f(x) = (4x^2-36x)/(x-9)

I don't really understand how to do this at all. Any help is appreciated.

Answer 1

where the function doesn't have a continuous line, that is where it jumps or is undefined
like if x = 9, x-9 will make the denominator 0, thus undefined, so, x cannot be = 9

Answer 2

$$
\frac{4x^2-36x}{x-9} \implies
\frac{4x(x-9)}{x-9}
$$

Answer 3

getting common factor

Answer 4

\(\cfrac{4x(x-9)}{x-9} = 0\)

Answer 5

so, it seems to be the line y = 4x, with a "hole" in x = 9, the zeros, would be the origin