Understanding Functions and the Vertical Line Test

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, it 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 the purpose of the vertical line test?

• To find the slope of a graph

• To check if a graph represents a function

• To determine if a graph is a straight line

• To identify the x-intercepts of a graph

Which statement best describes a function?

• Every x-value can have multiple y-values

• Every y-value can have multiple x-values

• Every x-value has exactly one y-value

• Every y-value has exactly one x-value

What happens if a vertical line intersects a graph at more than one point?

• The graph is a linear function

• The graph is a quadratic function

• The graph is not a function

• The graph is a function

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

• Because it is a straight line

• Because no vertical line intersects it more than once

• Because it has multiple y-values for each x-value

• Because it is a circle

Why does the second graph fail the vertical line test?

• It is a straight line

• It has multiple x-values for each y-value

• Vertical lines intersect it at multiple points

• It is a parabola

What is the result of the vertical line test on a circle?

• The circle passes the test

• The circle fails the test

• The circle is a function

• The circle is a linear function

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

• The graph is not a function

• The graph is a function

• The graph is a quadratic function

• The graph is a cubic function

What does it mean if an x-value has two different y-values?

• The graph is not a function

• The graph is a constant function

• The graph is a linear function

• The graph is a function

How does the vertical line test relate to the definition of a function?

• It shows that every y-value has one x-value

• It confirms that every x-value has one y-value

• It proves that every x-value has multiple y-values

• It demonstrates that every y-value has multiple x-values