Question

A student was asked to decide whether the function below is linear or nonlinear using both a table and a graph. 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=5*x^(2)

Answer 1

The student is incorrect in claiming that the function is nonlinear. The function y = 5x^2 is indeed a quadratic function, which is a type of nonlinear function. It is incorrect to state that the rate of change is constant in this function because the rate of change is not constant. When the input value (x) changes by 1, the output value (y) changes by 5 times the square of that change. This means that the rate of change varies depending on the value of x, which is characteristic of a nonlinear function. The student may have mistakenly assumed that linear functions have a constant rate of change, leading to their incorrect conclusion.