If the ratios of consecutive y-values are equal, then the data can be modeled by an exponential function. If the difference of consecutive y-values is constant, then the data can be modeled by a linear function.
Linear function
Practice makes perfect
We want to check whether the given table represents a linear or an exponential function. If the ratios of consecutive y-values are equal, then the data represents an exponential function. If the difference of consecutive y-values is constant, then the data represents a linear function. Consider the given table.
x
y
1
- 2
2
0
3
2
4
4
Notice that the difference between each x-value is 1. Let's calculate the difference between consecutive y-values.
0-(- 2)= 2, 2-0= 2, 4-2= 2
Each difference is equal to 2. Since the x-values are at regular intervals and the y-values differ by a constant, the table represents a linear function.
