Answer
The intercepts are: (0,−9), (−3,0), and (3,0).
Work Step by Step
In order to solve this problem, we will have to recall the following points:
(a) The intercepts of a function are those points where the graph crosses the $x-$ axis or the $y-$ axis.
(b) We set $y=0$ and then solve for $x$ in order to calculate the x-intercept.
(c) We set $x=0$ and then solve for $y$ in order to calculate the y-intercept.
Case 1: Let $y=0$ and then solve for $x$ to obtain:
$y=x^2-9 \\x^2=0-9 \implies x =\pm 3$
Therefore, the $x$-intercepts of the function are: $(-3,0)$ and $(3,0)$
Case 2: Let $x=0$ and then solve for $y$ to obtain:
$y=x^2-9 \\ y=0-9 \implies y=-9$
Therefore, the $y$-intercept of the function is: $(0,-9)$
