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

Answer:

Function 1 is linear and Function 2 is exponential.

Step-by-step explanation:

Function 1:

x       y

-3     0  

-1      6  

1       12  

3       18

Calculate the slope

Formula of slope :$m = \frac{y_2-y_1}{x_2-x_1}$

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

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

Substitute the values in the formula

$m = \frac{6-0}{-1-(-3)}$

$m = \frac{6}{2}$

$m = 3$

Now using another two points

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

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

Substitute the values in the formula

$m = \frac{18-12}{3-1}$

$m = \frac{6}{2}$

$m = 3$

Function 2:

x      y

1      13  

2     6.5  

3     3.25  

4     1.625

Calculate the slope

Formula of slope :$m = \frac{y_2-y_1}{x_2-x_1}$

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

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

Substitute the values in the formula

$m = \frac{6.5-13}{2-1}$

$m = \frac{-6.5}{2}$

$m = -3.5$

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

$m = \frac{1.625-2.5}{4-3}$

$m = \frac{-0.875}{1}$

$m = -0.875$

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.