Relations, Functions, 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

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 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 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 relation is not a function?

Back

A relation is not a function if at least one input (x-value) is associated with more than one output (y-value).

Front

Identify the range of the function represented by the graph: y = 2x + 3 for x in [-1, 2].

Back

The range is [1, 7].

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

Front

How can you determine if a set of ordered pairs is a function?

Back

Check if any x-value is repeated; if it is, the set is not a function.

Front

What is an example of a function?

Back

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

Front

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

Back

An example is {(1, 2), (1, 3)}, where the input 1 has two different outputs.