Linear vs Non-linear

Front

What is a linear function?

Back

A linear function is a function that has a constant rate of change and can be represented by a straight line on a graph.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not have a constant rate of change and cannot be represented by a straight line on a graph.

Front

How do you identify a linear function from an equation?

Back

If the equation can be written in the form y = mx + b, where m and b are constants, it is a linear function.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

If a function has a constant rate of change, what type of function is it?

Back

It is a linear function.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which creates a parabolic curve.

Front

What is the difference between linear and nonlinear graphs?

Back

Linear graphs are straight lines, while nonlinear graphs can be curves or other shapes.

Front

If Ted runs 1 block, then 2 blocks, then 4 blocks, then 8 blocks, what type of function is this?

Back

This is a nonlinear function because the distance he runs does not increase by a constant amount.

Front

What does it mean if a function is represented as y = 3x + 2?

Back

This is a linear function with a slope of 3 and a y-intercept of 2.