Identifying Functions

Front

What is a function?

Back

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

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line crosses the graph at more than one point, it is not a function.

Front

How can you tell if a relation is not a function?

Back

A relation is not a function if at least one input is related to more than one output.

Front

What does it mean for a table to represent a function?

Back

A table represents a function if each x-value corresponds to only one y-value.

Front

If a graph passes the vertical line test, what can you conclude?

Back

If a graph passes the vertical line test, it is a function.

Front

What is an example of a function?

Back

An example of a function is the equation y = 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 the set of points {(1, 2), (1, 3)}, where the input 1 is related to two different outputs.

Front

What is the definition of a domain in 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 definition of a range in a function?

Back

The range of a function is the set of all possible output values (y-values) that result from the 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 corresponds to only one y-value.