Question

How do you graph `y=(-4x^2)/(x^2-16)` using asymptotes, intercepts, end behavior?

Answer 1

`-4x2/(x^2-16)`

Vertical asymptote :
`x = +-4`

Horizontal asymptote :
`y = -4`

Slant asymptote : No slant or oblique asymptote.

X intercept : `y=0, x = 0`
Y intercept : `x = 0, y =0`

Explanation:

`-4x2/(x^2-16)`

Vertical asymptote : equate denominator to 0.
`x = +-4`

Horizontal asymptote : leading coefficients division
`y = -4`

Slant asymptote : No slant or oblique asymptote as degrees are same in numerator and denominator.

X intercept : `y=0, x = 0`
Y intercept : `x = 0, y =0`

End behavior

graph{-4x^2/(x^2-16) [-10, 10, -5, 5]}