Answer
$(a)$ See the image below.
$(b) $
$x$-intercepts - $A(-1,0)$, $C(1,0)$
$y$-intercepts - $B(0,1) $
$(c)$ Solving equation gives us points:
$x$-intercepts:
$x=-1$ ; $y=0$
$x=1$ ; $y=0$
$y$-intercepts
$x=0$ ; $y=1$
Work Step by Step
$(a)$ We simply input the equation and get the graph. See the image above.
$(b)$ As we clearly see from the graph, we have following interceptions:
x-intercepts - A(-1,0), C(1,0)
y-intercepts - B(0,1)
$(c)$ $y=\sqrt[3]{1-x^2}$
For x-intercept, we need to find x values where y=0
$\sqrt[3]{1-x^2}=0$
$1-x^2=0$
$x^2=1$
$x_1=-1$
$x_2=1$
For y-intercept, we need to find y values where x=0
$y=\sqrt[3]{1-0^2}=1$
