Answer:
Step-by-step explanation:
To find the x-intercept and y-intercept of the function f(x) = x²√25 - x², we need to set the function equal to 0 and solve for x, and then set x equal to 0 and solve for f(x) respectively.
x-intercept:
f(x) = 0
x²√25 - x² = 0
x²(√25 - 1) = 0
x² = 0 (since √25 - 1 ≠ 0)
x = 0
So, the x-intercept is at point (0, 0).
y-intercept:
x = 0
f(0) = 0²√25 - 0²
f(0) = 0
y = 0
So, the y-intercept is also at point (0, 0).
The graph of the function passes through the origin, and the x and y intercepts are both at point (0, 0).