A linear function can be represented in the form f(x) = mx + b.
The graph of a linear function extends infinitely in both directions.
The values of x and y in a linear table have a constant rate of change.
What is the difference between a linear function and a nonlinear function? Explain what each looks like when represented as a table and as a graph.
A linear function is a function where the graph of the function is a straight line. It can be represented in the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept. When represented as a table, the values of x and y will have a constant rate of change. When represented as a graph, the line will be a straight line that extends infinitely in both directions.
Sample Response: A linear function has a constant additive rate of change, while a nonlinear function does not. For a table of values to be linear, the dependent variable must have a constant rate of change as the independent variable increases by 1. On a graph, the function must be a straight line to be linear.
What did you include in your response? Check all that apply.
A linear function has a constant additive rate of change.
A nonlinear function does not have a constant additive rate of change.
The graph of a linear function is a straight line, while a nonlinear graph is curved.
The dependent variable in a linear table has a constant additive rate of change as the independent variable increases by 1.
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