Linear vs Non Linear Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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 can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line.

Front

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

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the output value when the input is zero.

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which graphs to a parabola.

Front

What is the difference between a linear and a nonlinear graph?

Back

A linear graph is a straight line, while a nonlinear graph can be curved or have bends.

Front

What does it mean for a function to have a constant rate of change?

Back

A function has a constant rate of change if the difference in the output values divided by the difference in the input values is the same for any two points on the function.