Functions vs. Not a Function & Linear vs. Nonlinear Flashcard

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 definition of a linear function?

Back

A linear function is a function that graphs to a straight line and has a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line and has a variable rate of change.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input has exactly one output.

Front

What does it mean for a function to have a constant rate of change?

Back

A constant rate of change means that the change in the output (y) is consistent for every change in the input (x).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented as (0, y).

Front

What is the slope of a linear function?

Back

The slope is a measure of the steepness of the line, calculated as the change in y divided by the change in x.

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 does it mean if a graph fails the vertical line test?

Back

If a graph fails the vertical line test, it means that there are multiple outputs for at least one input, indicating it is not a function.