1. For which interval is the function constant?
Which answer describes the function f(x) =2x^3−x^2?
The function is constant when its slope is zero.
When the slope is zero, as the value of x changes, the value of f(x) doesn't change.
For instance, when x = -2, f(x) = 2 . And when x = -3, f(x) = 2 .
We changed the value of x but the value of f(x) did not change.
So the function is constant on the interval (-4, 0)
f(x) = 2x3 − x2
To determine whether this function is even, odd, or neither, we need to find f(-x) .
f(-x) = 2(-x)3 – (-x)2
Since a negative number times a negative number is a positive number, (-x)2 = x2
f(-x) = 2(-x)3 – x2
A negative number multiplied by itself 3 times is a negative number, so...
f(-x) = -2x3 – x2
This is not the same as the original function, and it is not the same as -1 times the original function, so this function is neither.