A student was asked to decide whether the function below is linear or nonlinear using both a table and a graph. he 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

y=-x power of 2

x y
-2 blank
-1 blank
0 blank
1 blank
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Answer 1

The student made a mistake in their reasoning. The function y = -x^2 is actually a nonlinear function. Even though the rate of change (-2, 1, -2, 1) of the y-values is constant, the graph of the function is not a straight line. The graph is a downward-opening parabola. Therefore, the function is nonlinear.