Determine if a Relation is a Function or Not

Front

What is a function?

Back

A function is a relation where each input (or domain) has exactly one output (or range).

Front

How can you determine if a relation is a function?

Back

A relation is a function if no two ordered pairs have the same first element (input) with different second elements (outputs).

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

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

Given the relation {(0,2),(-2,2),(1,4),(4,1),(0,-1)}, which pair makes it not a function?

Back

(0,-1) makes it not a function because the input 0 has two outputs (2 and -1).

Front

If f(x) = 2x^2 - 8, what is the range when the domain is {-2,3,5}?

Back

The range is {0,10,42}.

Front

What is an example of a function represented in a table?

Back

A table where each x-value corresponds to only one y-value, e.g., (1,2), (2,3), (3,4).

Front

Which ordered pair would make a function no longer a function: (-4,1) or (1,-4)?

Back

(-4,1) would make it no longer a function if -4 is already paired with another y-value.

Front

What is a vertical line test?

Back

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.