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

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?

y = -6x^2

Complete the table of values for the function.

x  y
2 [ ]

1 [ ]

0 [ ]
  
1 [ ]
  
2 [ ]

GPT 3.5 · Answer

To complete the table of values for the function y = -6x^2, we need to substitute the given values of x into the equation and calculate the corresponding values of y.

x y
2 -24
1 -6
0 0
-1 -6
-2 -24

Now, let's analyze the table and the graph.

The student's claim that the function is nonlinear because the rate of change is constant is incorrect. In fact, a quadratic function such as y = -6x^2 is nonlinear because its graph is a curve, not a straight line. Therefore, the student made a mistake in identifying the function as nonlinear.