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

The first function is linear and the second is neither.

Explanation:

A linear function has a constant rate of change.

The rate of change is the slope; it is found using the formula

`m=(y_2-y_1)/(x_2-x_1)`

Between the first two points, the slope is

m = (31-11)/(3-1) = 20/2 = 10

Between the next two points, the slope is

m = (51-31)/(5-3) = 20/2 = 10

This function has a constant slope, so the function is linear.

In order for a function to be exponential, the percent change between y-values must be the same.

To find the percent of change, we use the formula

`\text{percent of change}=\frac{\text{amount of change}}{\text{original amount}}`

For the first two points, this is

(5-2)/2 = 3/2 = 1.5

For the next two points, this is

(9-5)/5 = 4/5 = 0.8

This is not the same; this means it is not an exponential function.