To determine whether a function is linear or nonlinear, we need to analyze the rate of change. If the rate of change is constant, the function is linear. If the rate of change is not constant, the function is nonlinear.
In this case, the student correctly observed that the rate of change is constant. However, they mistakenly concluded that the function is nonlinear because the graph of the function is not a line. The graph of a linear function will always be a straight line, but a nonlinear function can have a curved graph.
To confirm the linearity of the function, we can check if the difference in y-values is proportional to the difference in x-values.
From the given values, we have:
x: -2 --> -1: y: 1 --> 2
The difference in x-values is: -1 - (-2) = 1
The difference in y-values is: 2 - 1 = 1
Since the difference in y-values is equal to the difference in x-values, the function is indeed linear.
The student's mistake was concluding that the function is nonlinear based solely on the graph's appearance, without considering the constant rate of change.
Completing the table using the linear relationship between x and y-values:
X -2 -1 0 1 2
y 1 2 3 4 5
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? Complete the table of values for the function. X -2 -1 y 1 2
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