Final answer:
The x-intercepts of the function are x = 0, x = 0, and x = 0. The y-intercept is 0.
Step-by-step explanation:
The given function is f(x) = (x⁷)(x¹)(x²). To find the x-intercepts, set the function equal to zero and solve for x. Here, (x⁷)(x¹)(x²) = 0. Since any number multiplied by zero is zero, one of the factors must be zero. Therefore, the x-intercepts are x = 0, x = 0, and x = 0.
To find the y-intercept, substitute x = 0 into the function. f(0) = (0⁷)(0¹)(0²) = 0. Thus, the y-intercept is 0.