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.
The correct answer is: B. She said the rate of change is constant, but the rate of change is not constant.
The student may have made the mistake of assuming that the function is linear because the graph of the function is a line. However, a linear function must have a constant rate of change, which means that the graph should have a constant slope. If the rate of change is not constant, then the function is nonlinear. The answer choices A and C incorrectly state that the function is linear despite the rate of change not being constant. Option D is the correct choice as it accurately identifies the function as nonlinear due to the non-constant rate of change. Option C is not relevant to the mistake made by the student.
The correct answer is OC. The function is nonlinear because the rate of change is constant and the graph of the function is a line.
The mistake the student might have made is OC. She said the graph of the function is not a line, but it is a line.
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 consider the rate of change and the shape of the graph.
In a linear function, the rate of change is constant, meaning that the function increases or decreases at a consistent rate. The graph of a linear function is a straight line.
In a nonlinear function, the rate of change is not constant, meaning that the function does not increase or decrease at a consistent rate. The graph of a nonlinear function can take various shapes, such as curves or angles.
In this case, if the rate of change of the function is not constant and the graph is not a straight line, then the function is nonlinear.
Regarding the mistake the student might have made, the correct answer is OC. She said the graph of the function is not a line, but it is a line. This is a mistake because if the graph is not a straight line, then it is not a linear function.