Question

Drag and drop the answer into the box to identify each function as linear, exponential, or neither.

​x​ 1 3 5
f(x) 11 31 51
​x​ 0 2 4
f(x) 2 5 9

Answer 1

linear
linear
linear
neither

Answer 2

First function is linear.

Second function is neither.

Explanation:

To know if a function is linear, its points have to change with the same ration, which is called the slope.

If we try this for both function, we could know if they are linear.

First function

We are gonna calculate the slope for the first two points and the other two points.

`m=(31-11)/(3-1)=(20)/(2)=10\\  m=(51-31)/(5-3)=(20)/(2)=10`

As you can observe, the first function is linear, because points change with the same ratio of 10.

Second function.

We do the same with the second function to find out if it's linear.

`m=(5-2)/(2-0)=(3)/(2)\\  m=(9-5)/(4-2)=(4)/(2)=2`

This means that the second function is not linear. Let's find out if it's exponential then. To do that, we have to calculate its percentage of change (PC), to be an exponential function, the first two points and the last two points must have the same percentage of change (PC):

`PC=(major-minor)/(minor)\\PC=(5-2)/(2)=(3)/(2)\\\\\PC=(9-5)/(5)=(4)/(5)`

AS you can observe, the percentage of change is not the same.

This means that the second function is neither a linear function or exponential function.