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# Two Questions

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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

Mar 16, 2018

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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)  =  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.

Mar 16, 2018