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 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 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

Is the mapping {(1, 2), (2, 3), (1, 4)} a function?

Back

No, it is not a function because the input '1' has two different outputs (2 and 4).

Front

What does it mean if a function is defined as 'undefined'?

Back

It means that there is no output for a given input, often due to division by zero or other restrictions.

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 is the relation {(1, 2), (1, 3)}, where the input '1' has two outputs.

Front

How do you find the domain of a function given its equation?

Back

To find the domain, identify all x-values that can be input into the function without causing any mathematical errors (like division by zero).

Front

How do you find the range of a function given its graph?

Back

To find the range from a graph, look at the y-values covered by the graph.