Answer
$(a)$
$x$-intercept $A(-2,0)$ and $B(2,0)$
$y$-intercept $C(0,-2)$
See the Red graph on the image below. We have symmetry with respect to $y$-axis.
$(b)$
$x$-intercept $O(0,0)$
$y$-intercept $O(0,0)$
See the Blue graph on the image below. We have symmetry with respect to the origin.
Work Step by Step
$(a)$ $y=-\sqrt{4-x^2}$
$x$-intercept happens when $y=0$
$-\sqrt{4-x^2}=0$
$4-x^2=0$
$x^2=4$
$x=±2$
$A(-2,0)$ and $B(2,0)$
$y$-intercept happens when $x=0$
$y=-\sqrt{4-0^2}=-2$
$C(0,-2)$
We have three key points, so we can sketch the graph. See the Red graph on the image above.
We have symmetry with respect to $y$-axis. If we replace $x$ by $-x$ the equation will be the same as the original one.
$(b)$ $x=y^3$
$x$-intercept happens when $y=0$
$x=0^3$
$x=0$
$O(0,0)$
$y$-intercept happens when $x=0$
$y^3=0$
$y=0$
$O(0,0)$
Let's find $2$ more points for easier sketching:
$x=1$
$y^3=1$
$y=1$
$D(1,1)$
$x=-1$
$y^3=-1$
$y=-1$
$E(-1,-1)$
See the blue graph on the image above.
We have symmetry with respect to the origin.
