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 made a mistake in stating that the rate of change is constant. Looking at the table of values, we can see that as x increases by 1, the corresponding y-value decreases by a larger and larger amount. This means that the rate of change is not constant, indicating that the function is nonlinear.

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

Therefore, the student incorrectly determined that the function is nonlinear because they incorrectly assumed that the rate of change is constant. In reality, the rate of change is not constant, which makes this function nonlinear.