Functions & Function Notation

Front

What is a function?

Back

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

Front

How can you determine if a relation is a function using the vertical line test?

Back

If a vertical line intersects the graph of the relation at more than one point, then it is not a function.

Front

What does f(x) represent in function notation?

Back

f(x) represents the output of the function f for the input x, equivalent to y.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) for the function.

Front

If f(x) = 2x + 1, what is f(3)?

Back

f(3) = 2(3) + 1 = 7.

Front

What is the difference between a function and a relation?

Back

A relation can have multiple outputs for a single input, while a function cannot.

Front

What does it mean for a function to be linear?

Back

A linear function has a constant rate of change and can be represented by a straight line on a graph.

Front

What is an example of a non-function?

Back

The relation {(1, 2), (1, 3)} is not a function because the input 1 has two different outputs.

Front

How do you evaluate a function at a specific value?

Back

Substitute the specific value into the function's equation and simplify.