Identifying Functions

Front

What is a function?

Back

A function is a relation where every input has only ONE output.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b.

Front

What does it mean for a function to be nonlinear?

Back

A nonlinear function is a function that does not graph to a straight line, such as quadratic or exponential functions.

Front

Identify if the following relation is a function: {(1, 2), (2, 3), (1, 4)}

Back

Not a function, because the input '1' has two different outputs (2 and 4).

Front

Identify if the following relation is a function: {(1, 2), (2, 3), (3, 4)}

Back

Yes, it is a function, because each input has only 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 crosses the curve more than once, it is not a function.

Front

Give an example of a linear function.

Back

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

Front

Give an example of a nonlinear function.

Back

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

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for the function.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.