Using the Vertical Line Test for Functions

The video tutorial explains how to determine if graphs represent functions using the vertical line test. A function is defined as a relation where each input has exactly one output. The vertical line test is used to check this graphically: if a vertical line intersects a graph at more than one point, the graph is not a function. Several examples are provided, including graphs that pass and fail the test, such as a circle graph that fails because it has multiple outputs for a single input.

What is a function in mathematical terms?

• A relation where every output is paired with exactly one input.

• A relation where every output has multiple inputs.

• A relation where every input is paired with exactly one output.

• A relation where every input has multiple outputs.

What test can be used to determine if a graph represents a function?

• Curve Test

• Vertical Line Test

• Slope Test

• Horizontal Line Test

What does it mean if a vertical line intersects a graph in more than one point?

• The graph is a straight line.

• The graph does not represent a function.

• The graph represents a function.

• The graph is a circle.

In the first example graph, why is it considered a function?

• Because no vertical line intersects the graph in more than one point.

• Because it is a circle.

• Because it is a straight line.

• Because it has multiple outputs for each input.

In the second example graph, why does it fail the Vertical Line Test?

• Because it is a circle.

• Because vertical lines intersect the graph in more than one point.

• Because it has only one output for each input.

• Because it is a straight line.

What happens at the x-value of 2 in the second example graph?

• There are three corresponding y-values.

• There are no corresponding y-values.

• There is only one corresponding y-value.

• There are two corresponding y-values.

In the third example graph, why is it considered a function?

• Because no vertical line intersects the graph in more than one point.

• Because it has multiple outputs for each input.

• Because it is a circle.

• Because it is a straight line.

Why does the circle graph fail the Vertical Line Test?

• Because vertical lines intersect the graph in more than one point.

• Because it is a function.

• Because it is a straight line.

• Because it has only one output for each input.

At the x-value of 0 in the circle graph, what are the outputs?

• +2 and -2

• +4 and -4

• +1 and -1

• +3 and -3

What is the main reason a graph fails the Vertical Line Test?

• It is a function.

• It has no outputs.

• It has multiple outputs for a single input.

• It is a straight line.