A student was asked to decide whether the function below is linear or nonlinear using both a table and a graph. She said the function is nonlinear because the rate of change is constant and the graph of the function is not a line. Decide whether the function is linear or nonlinear using both a table and a graphWhat mistake might the student have made?
y=6x2
Complete the table of values for the function.
X
-2
-1
0
1
2
y
The student's mistake is in stating that the rate of change is constant for this function. In a linear function, the rate of change is constant, meaning that the change in y is always proportional to the change in x. However, in this function, the rate of change is not constant. As x increases by 1, y increases by 6 multiplied by that value of x squared. Therefore, the rate of change is not constant, indicating that the function is nonlinear.
Completing the table of values for the function:
X | y
-2 | 24
-1 | 6
0 | 0
1 | 6
2 | 24