Answer
x-intercepts: -3 and 3
y-intercepts: -2 and 2
Work Step by Step
RECALL:
(i) The x-intercept is the value of x when y=0.
(ii) The y-intercept is the value of y when x=0.
Based on the given graph of the function, it appears that the function has:
x-intercepts: -3 and 3
y-intercepts: -2 and 2
Check if these are the actual intercepts by substituting each one to the given equation:
For x=-3:
$\\\frac{(-3^2)}{9}+\frac{0^2}{4}=1
\\\frac{9}{9}+0=1
\\1=1$
For x=3:
$\\\frac{3^2}{9}+\frac{0^2}{4}=1
\\\frac{9}{9}+0=1
\\1=1$
Thus, -3 and 3 are x-intercepts of the equation.
For y=-2:
$\\\frac{0^2}{9}+\frac{(-2)^2}{4}=1
\\0+\frac{4}{4}=1
\\1=1$
For y=2:
$\\\frac{0^2}{9}+\frac{2^2}{4}=1
\\0+\frac{4}{4}=1
\\1=1$
Thus, -2 and 2 are y-intercepts of the equation.