11-10-22 Relations, Functions, Domain and Range (Alg)

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 graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

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

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

Back

Yes, because each x-value has only one corresponding y-value.

Front

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

Back

No, because the x-value 1 has two different y-values (2 and 3).

Front

What does it mean if a function is not one-to-one?

Back

A function is not one-to-one if there are at least two different x-values that produce the same y-value.

Front

Given the relation {(-1,2), (-2,4), (2,5), (0,-2)}, what is the domain?

Back

The domain is {-1, -2, 2, 0}.

Front

Given the relation {(-1,2), (-2,4), (2,5), (0,-2)}, what is the range?

Back

The range is {2, 4, 5, -2}.

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a graph is a function by checking if any vertical line intersects the graph more than once.