Identifying 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 a linear function?

Back

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

Front

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

Back

A linear function will have a constant rate of change, meaning the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

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/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

What is the vertical line test?

Back

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

Front

What is an example of a linear function?

Back

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

Front

What is an example of a nonlinear function?

Back

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

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.