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?
The student made a mistake in their reasoning. The function y = 5x^2 is actually nonlinear. Although the rate of change is constant, it is important to note that for a function to be linear, the highest exponent of the variable (in this case x) must be 1. In the given function, the highest exponent of x is 2, thus making the function nonlinear. The student may have confused the idea of a constant rate of change with linearity, leading to their incorrect conclusion.
