How do you graph y=(-4x^2)/(x^2-16)y=4x2x216 using asymptotes, intercepts, end behavior?

1 Answer
Oct 17, 2017

-4x2/(x^2-16)4x2x216

Vertical asymptote :
x = +-4x=±4

Horizontal asymptote :
y = -4y=4

Slant asymptote : No slant or oblique asymptote.

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

Explanation:

-4x2/(x^2-16)4x2x216

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

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

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

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

End behavior

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