Decide whether the function is linear or nonlinear. Explain. Choose the correct answer below. A. The function is linear because the rate of change is constant and the graph of the function is a line. B. The function is linear because the rate of change is not constant and the graph of the function is not a line. OC. The function is nonlinear because the rate of change is constant and the graph of the function is a line. D. The function is nonlinear because the rate of change is not constant and the graph of the function is not a line. What mistake might the student have made? OA. She said the function is nonlinear, but the function is linear. B. She said the rate of change is constant, but the rate of change is not constant. OC. She said the graph of the function is not a line, but it is a line.

Question

Decide whether the function is linear or nonlinear. Explain. Choose the correct answer below. A. The function is linear because the rate of change is constant and the graph of the function is a line. B. The function is linear because the rate of change is not constant and the graph of the function is not a line. OC. The function is nonlinear because the rate of change is constant and the graph of the function is a line. D. The function is nonlinear because the rate of change is not constant and the graph of the function is not a line. What mistake might the student have made? OA. She said the function is nonlinear, but the function is linear. B. She said the rate of change is constant, but the rate of change is not constant. OC. She said the graph of the function is not a line, but it is a line.

Answer 1

The correct answer is D. The function is nonlinear because the rate of change is not constant and the graph of the function is not a line.

The student might have mistaken the function to be linear because they incorrectly assumed that the rate of change is constant and the graph of the function is a line.

Answer 2

The correct answer is D. The function is nonlinear because the rate of change is not constant and the graph of the function is not a line.

To determine whether a function is linear or nonlinear, we need to analyze the rate of change and the shape of its graph.

In a linear function, the rate of change is constant, meaning the function's value changes by the same amount for equal intervals of input values. The graph of a linear function is always a straight line.

On the other hand, a nonlinear function does not have a constant rate of change. The function's value may change at different rates depending on the input value. This results in a graph that is not a straight line.

In this question, the student mistakenly identified the function as nonlinear. However, the student did correctly identify that the rate of change is not constant and that the graph of the function is not a line. Therefore, the mistake made by the student is not choosing option A but opting for option C instead.