How do you sketch y = x^4 / x^2 - 1 ?

Question

How do you sketch this Rational Function?

(by finding the asymptotes, zeros...)

Answer 1

Greetings,

The vertical asymptotes occur at

x^2 - 1 = 0

(x + 1)(x - 1) = 0

x = -1 or x = 1

zero occurs at x^4 = 0

x = 0

The function is symmetrical about the y-axis,

as x -> inf,  y -> x^2

x^4/[(x + 1)(x - 1)]

----o+++++(x + 1)

----------o++(x - 1)

....-1....1

y is positive when x > 1 or x < -1

y is negative when -1 < x < 1

Regards