Answer
The y-intercept is 0
The x-intercepts are -1, 0, and 1
$\lim\limits_{x \to \infty} (x^4-x^6) = -\infty$
$\lim\limits_{x \to -\infty} (x^4-x^6) = -\infty$
Work Step by Step
$y = x^4-x^6$
When $x=0$, then $~~y = (0)^4-(0)^6 = 0$
When $y=0$:
$x^4-x^6 = 0$
$x^4(1-x^2) = 0$
$x^4(1-x)(1+x) = 0$
$x = 0, 1,-1$
$\lim\limits_{x \to \infty} (x^4-x^6)$
$=\lim\limits_{x \to \infty} x^4(1-x^2)$
$ = -\infty$
$\lim\limits_{x \to -\infty} (x^4-x^6)$
$=\lim\limits_{x \to -\infty} x^4(1-x^2)$
$ = -\infty$
