Identifying Functions from Tables and Points

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 from a set of points?

Back

A relation is a function if no two points have the same x-value with different y-values.

Front

Given the points (6,-5), (7,-3), (8,-1), (9,1), is this relation a function?

Back

Yes, this relation is a function because all x-values are unique.

Front

What does it mean if a relation is 'not a function'?

Back

It means that at least one x-value is associated with more than one y-value.

Front

Given the points (1,2), (1,3), (2,4), is this relation a function?

Back

No, this relation is not a function because the x-value 1 corresponds to two different y-values (2 and 3).

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, the relation is not a function.

Front

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

Back

No, it is not a function because the x-value 3 has two different y-values (4 and 5).

Front

What is an example of a function?

Back

An example of a function is the relation defined by the equation y = 2x + 3.

Front

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

Back

An example is the relation defined by the equation y^2 = x, which fails the vertical line test.

Front

How can you represent a function using a table?

Back

A function can be represented in a table by listing pairs of x and y values, ensuring each x-value is unique.