Answer
The x-intercepts are x=-8 and x=8
The y-intercepts are y=4
Work Step by Step
(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: -8 and 8
y-intercept: 4
Check if these are the actual intercepts by substituting each one to the given equation: x^2 + y^3 - (x^2)(y^2) = 64
For x=-8:
-8^2 + 0^3 - (-8^2)(0^2) = 64
For x=8:
8^2 + 0^3 - (8^2)(0^2) = 64
Thus, -8 and 8 are x-intercepts of the equation.
For y=4:
0^2 + 4^3 - (0^2)(4^2) = 64
Thus, 4 is the y-intercept of the equation.