Question

Classify each function shown in the tables below as either linear or exponential.

A) The following function is x y
-3 0
-1 6
1 12
3 18
B) The following function is x y
1 13
2 6.5
3 3.25
4 1.625

Answer 1

A is linear ( the graph would be a line with slope 3)
Note that as x increases by 2 y increases by 6.

Answer 2

Function 1 is linear and Function 2 is exponential.

Explanation:

Function 1:

x y

-3 0

-1 6

1 12

3 18

Calculate the slope

Formula of slope :
`m = (y_2-y_1)/(x_2-x_1)`

`(x_1,y_1)=(-3,0)`

`(x_2,y_2)=(-1,6)`

Substitute the values in the formula

`m = (6-0)/(-1-(-3))`

`m = (6)/(2)`

`m = 3`

Now using another two points

`(x_1,y_1)=(1,12)`

`(x_2,y_2)=(3,18)`

Substitute the values in the formula

`m = (18-12)/(3-1)`

`m = (6)/(2)`

`m = 3`

Function 2:

x y

1 13

2 6.5

3 3.25

4 1.625

Calculate the slope

Formula of slope :
`m = (y_2-y_1)/(x_2-x_1)`

`(x_1,y_1)=(1,13)`

`(x_2,y_2)=(2,6.5)`

Substitute the values in the formula

`m = (6.5-13)/(2-1)`

`m = (-6.5)/(2)`

`m = -3.5`

Now using another two points

`(x_1,y_1)=(3,2.5)`

`(x_2,y_2)=(4,1.625)`

Substitute the values in the formula

`m = (1.625-2.5)/(4-3)`

`m = (-0.875)/(1)`

`m = -0.875`

In Function 1 slope remains same with distinct points.

In Function 2 Slope varies with distinct points

Thus Function 1 is linear and Function 2 is exponential.