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 does not require that each input has only one output.

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 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

Given the function {(0,1), (1,-3), (2,-4), (-4,1)}, what is the domain?

Back

D: {0, 1, 2, -4}.

Front

Given the function {(0,1), (1,-3), (2,-4), (-4,1)}, what is the range?

Back

R: {1, -3, -4}.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if each x-value is paired with only one y-value.

Front

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

Back

No, if a function has two y-values for the same x-value, it is not a function.

Front

What is an example of a function?

Back

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