3-2 Functions and Relations

Front

What is a function?

Back

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

Front

What is a relation?

Back

A relation is a set of ordered pairs, which can include functions but may also have inputs with multiple outputs.

Front

How can you determine if a graph represents a function?

Back

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

Front

What does it mean if a relation has two y-values for one x-value?

Back

It means the relation is not a function, as each input must have only one output.

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 a table shows the pairs (1, 2), (2, 3), (1, 4), is it a function?

Back

No, because the input 1 has two outputs (2 and 4).

Front

What is the vertical line test?

Back

A method to determine if a graph is a function by checking if a vertical line crosses the graph more than once.

Front

Can a function have a domain of all real numbers?

Back

Yes, a function can have a domain of all real numbers if there are no restrictions on the input values.

Front

What is an example of a function?

Back

An example is f(x) = 2x + 3, where each x-value has a unique y-value.