Domain, Range, and Functions

Front

What is a function?

Back

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

Front

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is paired with more than one y-value.

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

What does it mean if a function has a range of all real numbers?

Back

It means that the function can output any real number value.

Front

What is an example of a non-function relation?

Back

A relation where the x-value 11 is paired with both y-values 2 and 3 is a non-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 crosses the graph more than once, it is not a function.

Front

What is the significance of the range [-15, ∞)?

Back

This range indicates that the lowest output value is -15, and the function can output any value greater than or equal to -15.

Front

Can a function have a domain of all real numbers?

Back

Yes, a function can have a domain of all real numbers if it accepts any real number as input.

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.