Linear and Non-Linear Functions

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It has a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. It has a variable rate of change.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values.

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) where b is the y-value.

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.

Front

What does it mean if a function has a constant rate of change?

Back

It means that for every unit increase in x, the value of y increases by a fixed amount.

Front

How do you find the rate of change from a graph?

Back

The rate of change can be found by selecting two points on the line and using the formula (y2 - y1) / (x2 - x1).

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 when graphed.

Front

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

Back

A linear equation can be written in the form y = mx + b, while a nonlinear equation cannot be expressed in this form.