2.6 Formulaizing Relations and Functions

Front

What is a function?

Back

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

Front

What is the definition of domain in a function?

Back

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

Front

What is the definition of range in a function?

Back

The range is the set of all possible y-values (outputs) for a function.

Front

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

Back

A relation is a function if each input is associated with exactly one output.

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 horizontal line test?

Back

The horizontal line test determines if a function is one-to-one; if a horizontal line intersects the graph more than once, it is not one-to-one.

Front

What happens if x-values repeat in a set of ordered pairs?

Back

If x-values repeat, the relation is not a function.

Front

What happens if y-values repeat in a set of ordered pairs?

Back

If y-values repeat, the relation can still be a function as long as each x-value has only one corresponding y-value.

Front

Can a straight line be a function?

Back

Yes, a straight line can be a function if it passes the vertical line test.

Front

What is an example of a non-function?

Back

A relation where a single x-value corresponds to multiple y-values, such as a circle.