Linear and Non-Linear Functions

Front

What is the rate of change?

Back

The rate of change is the ratio of the change in the output value to the change in the input value, often represented as the slope of a line.

Front

Slope is another word for:

Back

Rate of Change

Front

What is the rate of change when the output changes from 0 to 3 and the input changes from 1 to 4?

Back

The rate of change is 1.

Front

What are the outputs of the function represented by the table?

Back

Outputs are the values that result from applying the function to the inputs.

Front

Is the function represented by the table linear or nonlinear?

Back

Nonlinear functions do not have a constant rate of change.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and has a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line and has a variable rate of change.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the output when the input is zero.

Front

What is the formula for a linear function?

Back

The formula for a linear function is y = mx + b, where m is the slope and b is the y-intercept.