Domain and Range of Functions

Front

What is the definition of a function?

Back

A function is a relation in which each input (x-value) is associated with exactly one output (y-value).

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

How can you determine if a relation is a function?

Back

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

Front

What does it mean if a function has a domain of -4 < x ≤ 6?

Back

It means that the function is defined for all x-values greater than -4 and up to and including 6.

Front

Give 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 is paired with two different y-values.

Front

What is the significance of the x-value in a function?

Back

The x-value is the input of the function, and it determines the corresponding y-value (output) based on the function's rule.

Front

What does it mean for a function to be defined?

Back

A function is defined when there is a clear rule that assigns exactly one output for each input.