Vertical Line Test

Front

What is the Vertical Line Test?

Back

A method used 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 does it mean for a relation to be a function?

Back

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

Tags

CCSS.8.F.A.1

Front

If a vertical line intersects a graph at only one point, what can we conclude?

Back

The graph represents a function.

Front

What is an example of a function?

Back

The equation y = 2x + 3 is a function because for every x-value, there is one corresponding y-value.

Tags

CCSS.8.F.A.1

Front

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

Back

The equation x^2 + y^2 = 1 is not a function because a vertical line can intersect it at two points.

Front

How can you visually identify a function using a graph?

Back

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

Front

What is the significance of the x-value in a function?

Back

The x-value (input) must correspond to only one y-value (output) in a function.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Front

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value has only one y-value.

Tags

CCSS.8.F.A.1

Front

What is a common misconception about functions?

Back

A common misconception is that a function cannot have repeated y-values; however, it can, as long as each x-value is unique.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Front

What does it mean if a graph fails the vertical line test?

Back

It means that the graph does not represent a function because at least one x-value corresponds to multiple y-values.