Linear vs. Nonlinear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation 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, and can include curves, parabolas, and other shapes.

Front

What does the slope of a line represent?

Back

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

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x to 0 in the equation and solve for y.

Front

What is the y-intercept in the equation y = -4x - 5?

Back

The y-intercept is -5.

Front

What is the definition of a function?

Back

A function is a relation where every input (x-value) has exactly one output (y-value).

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is paired with one and only one output.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, y also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, y decreases.

Front

What is the standard form of a linear equation?

Back

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