Linear and Nonlinear Functions

Front

What is a function?

Back

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

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. Its general form is 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 form a straight line when graphed. Its output does not change at a constant rate.

Front

How can you determine if a set of ordered pairs is a function?

Back

A set of ordered pairs is a function if no two pairs have the same first element (x-value).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input has exactly one output.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the x-values increase, the y-values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the x-values increase, the y-values decrease.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented by the value of y when x = 0.