Linear vs Nonlinear 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 can have curves or varying rates of change.

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by its straight line graph, which has a constant slope.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function, indicating how much the output value changes for a unit change in the input value.

Front

What is the general form of a linear equation?

Back

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

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means that as the input increases, the output decreases.

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

Back

A constant rate of change means that the output value changes by the same amount for each unit increase in the input value, characteristic of linear functions.

Front

How do you determine if a function is linear or nonlinear from a table of values?

Back

If the differences between consecutive output values are constant for equal input intervals, the function is linear; otherwise, it is nonlinear.