Identify Functions (vertical line test)

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a curve is a graph of a function. If any vertical line intersects the graph at more than one point, then the graph is not a function.

Front

If a graph passes the vertical line test, what can we conclude?

Back

If a graph passes the vertical line test, we can conclude that it represents a function.

Front

What does it mean if a graph does not pass the vertical line test?

Back

If a graph does not pass the vertical line test, it means that there are at least two points on the graph that have the same x-coordinate, indicating it is not a function.

Front

Can a vertical line be part of a function?

Back

No, a vertical line cannot be part of a function because it would fail the vertical line test by intersecting the graph at multiple points.

Front

What is an example of a function?

Back

An example of a function is the equation y = 2x + 3, where each x value corresponds to exactly one y value.

Front

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

Back

An example of a relation that is not a function is the equation x^2 + y^2 = 1 (a circle), where multiple y values correspond to the same x value.

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

How can you determine the domain of a function from its graph?

Back

You can determine the domain of a function from its graph by identifying all the x-values for which the graph has points.