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

x y
2 [ ]

1 [ ]

0 [ ]

1 [ ]

2 [ ]

Answer 1

The student's mistake is stating that the rate of change is constant. In reality, the rate of change for the function y = -6x^2 is not constant. When we plug in different x-values into the function, we get different y-values. For example, when x = 2, y = -6(2)^2 = -6(4) = -24. But when x = 1, y = -6(1)^2 = -6. The rate of change between these two points is not constant.

Additionally, the graph of the function y = -6x^2 is a downward-opening parabola, not a straight line. This confirms that the function is nonlinear.

Therefore, the correct conclusion is that the function y = -6x^2 is nonlinear.