1. For which interval is the function constant?

(−4, 0)

(−∞, −4)

(4, ∞)

(0, 4)

Graph:

2.

Which answer describes the function f(x) =2x^3−x^2?

even

odd

neither

Guest Mar 16, 2018

#1**+2 **

**1.**

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)

**2.**

f(x) = 2x^{3} − x^{2}

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} = x^{2}

f(-x) = 2(-x)^{3} – x^{2}

A negative number multiplied by itself 3 times is a negative number, so...

f(-x) = -2x^{3} – x^{2}

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.

hectictar
Mar 16, 2018