Determine if a Relation is a Function or Not

Front

What is a function?

Back

A relation where each input has exactly one output.

Front

Which graph represents a function?

Back

A graph that passes the vertical line test.

Front

What is the vertical line test?

Back

If a vertical line intersects a graph at more than one point, the graph is not a function.

Front

Given the relation {(1, 2), (2, 3), (3, 4)}, is it a function?

Back

Yes, each input has exactly one output.

Front

Given the relation {(1, 2), (1, 3)}, is it a function?

Back

No, the input 1 has two different outputs.

Front

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

Back

It means that at least one input is associated with more than one output.

Front

If a relation has the pairs (2, 5), (3, 5), (4, 6), is it a function?

Back

Yes, each input has exactly one output.

Front

What is an example of a function?

Back

f(x) = x + 2 is a function because each x-value has one corresponding y-value.

Front

What is an example of a relation that is not a function?

Back

The relation {(1, 2), (1, 3)} is not a function because the input 1 has two outputs.

Front

How can you determine if a graph is a function?

Back

Use the vertical line test; if a vertical line crosses the graph more than once, it is not a function.