Question

1. (l2) state whether the following are linear or exponential functions.

a.

x	g(x)
-1	-8
0	-5
1	-2
2	1
3	4
4	7

linear or exponential (circle one)
how do you know?

Explanation:

Step1: Check for constant difference

Find the differences in $y -$ values ($g(x)$).
$g(0)-g(-1)=- 5-(-8)=3$; $g(1)-g(0)=-2 - (-5)=3$; $g(2)-g(1)=1-(-2)=3$; $g(3)-g(2)=4 - 1=3$; $g(4)-g(3)=7 - 4=3$.

Step2: Recall function - type rules

A linear function has a constant difference in $y -$ values for a constant difference in $x -$ values. Here, the difference in $x$ values is 1 each time, and the difference in $y$ values is 3 each time.

Answer:

Linear. The function has a constant first - difference of 3 for a constant difference of 1 in the $x$ values.