Question

How do you graph `g(x) = (x-4)^2/(x+2)`?

Answer 1

x=4 is a zero of the function
`g(x)=(x-4)^2/(x+2)`
while, x = -2 is an asymptote of the function

Explanation:

The given function is
`g(x)=(x-4)^2/(x+2)`
By inspection, the denominator
`x+2=0, when x = -2`
Thus,
`x = -2`
forms an asymptote where the function reaches a value infinity
The numerator is a function `(x-4)^2`
which has zero which is unique and at `x = 4`
These concepts described form a strong understanding of how to draw the graph of the function
`g(x)=(x-4)^2/(x+2)`