Linear vs Non Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line. Its graph can be a curve or any shape that is not a straight line.

Front

How can you identify a linear function?

Back

A linear function can be identified by its constant rate of change, meaning that the difference in y-values divided by the difference in x-values is the same for any two points.

Front

How can you identify a nonlinear function?

Back

A nonlinear function can be identified by its changing rate of change, meaning that the difference in y-values divided by the difference in x-values varies between points.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

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 value of y when x is 0.

Front

Give an example of a linear function.

Back

An example of a linear function is f(x) = 2x + 3.

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is f(x) = x^2.

Front

What role do exponents play in identifying nonlinear functions?

Back

Exponents indicate that the function is nonlinear; for example, x^2 is nonlinear because it does not form a straight line.