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1. For which interval is the function constant?

 

(−4, 0)

(−∞, −4)

(4, ∞)

(0, 4)

 

Graph:

A grid with x axis increments of two increasing from negative ten to ten and y axis increments of two increasing from negative ten to ten. The grid contains a continuous piecewise function with three vertices. The piecewise function passes from left to right through points begin ordered pair negative ten comma six end ordered pair, begin ordered pair negative four comma two end ordered pair, begin ordered pair zero comma two end ordered pair, begin ordered pair four comma negative four end ordered pair, and begin ordered pair eight comma two end ordered pair.

 

2. 

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

 

even

odd

neither

 Mar 16, 2018
 #1
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+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)  =  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

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