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 graph. What mistake might the student have​ made?

Question

x y
2
  

1
  

0
  
1
  
2

Answer 1

To determine whether a function is linear or nonlinear, we can examine if the rate of change is constant. If the rate of change is constant, the function is linear. If the rate of change is not constant, the function is nonlinear.

Based on the given table, the x-values are 2, 1, 0, 1, and 2. The corresponding y-values are missing. Without the y-values, we cannot calculate the rate of change between consecutive points. Therefore, we cannot determine if the rate of change is constant or not. Consequently, we cannot classify the function as linear or nonlinear based on the table alone.

Regarding the student's claim that the graph of the function is not a line, we don't have the information about the graph. If the graph is not provided, we cannot make any conclusion regarding the linearity or nonlinearity of the function based on the graph alone.

Hence, the student's mistake was concluding that the function is nonlinear based solely on the rate of change being constant and the graph not being a line, without examining the actual values or the graph.