How can you tell by looking at a table if its quadratic, linear or exponential?
For ex.
x: -2, -1, 0, 1, 2
y: 6, 1, 0, 1, 6
x y
-
10
-
40
-
9
-
35
-
8
-
30
-
7
-
25
-
6
-
20
To determine if a table represents a quadratic, linear, or exponential relationship, you can examine the pattern of the y-values (dependent variable) as the x-values (independent variable) change.
In the given example:
x: -2, -1, 0, 1, 2
y: 6, 1, 0, 1, 6
1. Linear Relationship: In a linear relationship, the y-values change by a constant rate as the x-values increase or decrease. To check if it's linear, calculate the differences between consecutive y-values. If the differences are the same, a linear relationship is likely present.
Calculating the differences:
1 - 6 = -5
0 - 1 = -1
1 - 0 = 1
6 - 1 = 5
As the differences are not consistent (-5, -1, 1, 5), it does not seem to be a linear relationship.
2. Exponential Relationship: In an exponential relationship, the y-values change by a constant multiplicative factor as the x-values increase or decrease. To check if it's exponential, calculate the ratios between consecutive y-values. If the ratios are the same, an exponential relationship is likely present.
Calculating the ratios:
6 ÷ 1 = 6
1 ÷ 0 = Undefined (division by zero)
0 ÷ 1 = 0
1 ÷ 6 = 0.1667
As the ratios are not consistent (6, undefined, 0, 0.1667), it does not seem to be an exponential relationship.
3. Quadratic Relationship: In a quadratic relationship, the y-values change according to a quadratic function where the differences between consecutive y-values form a consistent pattern. To check if it's quadratic, calculate the differences between consecutive differences. If those second differences are the same, a quadratic relationship is likely present.
Calculating the second differences:
(-1) - (-5) = 4
1 - (-1) = 2
5 - 1 = 4
As the second differences are the same (4, 2, 4), it appears to follow a quadratic relationship.
Based on the analysis, the given table seems to represent a quadratic relationship.