Linear and Nonlinear Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and can be represented by a straight line, while nonlinear functions do not have a constant rate of change and can be represented by curves.

Front

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

Back

A linear function will show a constant difference in the output values for equal increments in the input values.

Front

What is the general form of a linear function?

Back

The general form of a linear function 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 and can include quadratic, exponential, and other types of relationships.

Front

What is the slope of a linear function?

Back

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

Front

What does it mean for a relation to be a function?

Back

For a relation to be a function, each input must correspond to exactly one output.

Front

Can a function be both linear and nonlinear?

Back

No, a function cannot be both linear and nonlinear; it must fit into one of these categories based on its characteristics.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola.

Front

How can you determine if a graph represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.