3-1 Identify Functions and Domain and Range

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 set of ordered pairs is a function?

Back

A set of ordered pairs is a function if no two pairs have the same first element (x-value) with different second elements (y-values).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

What does it mean if a graph passes the vertical line test?

Back

If a graph passes the vertical line test, it means that for every x-value, there is only one corresponding y-value, indicating it is a function.

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 is at least one x-value that corresponds to multiple y-values, indicating it is not a function.

Front

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value has only one y-value.

Front

What is an example of a function?

Back

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

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the x-value 1 has two different y-values.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, typically in the form f(x) = mx + b.