Answer:
Its x-intercepts will be at 0, 9 and -9.
For the end behavior, because it's cubic and subtracts a multiple of x¹, this curve will primarily have a positive slope, but briefly a negative one when x is very near zero.
Step-by-step explanation:
We can factor this fairly easily, as both terms are divisible by 5x. After factoring those out they become a difference of squares, giving us all three factors of the function:
[tex]f(x) = 5x^3 - 90x\\f(x) = 5x(x^2 - 18)\\f(x) = 5x(x + 9)(x - 9)[/tex]
With that we can say that its x-intercepts will be at 0, 9 and -9.
Being a cubic function with a positive coefficient on the first term, we know that this curve will primarily have a positive slope, but briefly a negative one when x is very near zero.
