key term - Vertical Line Test

Definition

The vertical line test is a graphical method used to determine whether a relation or function is a function. It involves drawing a vertical line through the graph and checking if the line intersects the graph at only one point for each value of the independent variable.

5 Must Know Facts For Your Next Test

1. The vertical line test is used to determine if a relation is a function by checking if any vertical line intersects the graph at more than one point.
2. If a vertical line intersects the graph at only one point for each value of the independent variable, then the relation is a function.
3. If a vertical line intersects the graph at more than one point for any value of the independent variable, then the relation is not a function.
4. The vertical line test is particularly useful when dealing with transformations of functions, as it can help identify whether the transformed function is still a function.
5. The vertical line test is also important in the context of inverse functions, as a relation is a function if and only if its inverse is also a function.

Review Questions

• Explain how the vertical line test can be used to determine if a relation is a function.
  • The vertical line test is used to determine if a relation is a function by drawing a vertical line through the graph of the relation. If the vertical line intersects the graph at only one point for each value of the independent variable, then the relation is a function. If the vertical line intersects the graph at more than one point for any value of the independent variable, then the relation is not a function.
• Describe how the vertical line test is related to the concepts of domain and range.
  • The vertical line test is closely related to the concepts of domain and range. The domain of a function is the set of all possible input values, and the range is the set of all possible output values. By applying the vertical line test, we can determine if a relation is a function, which means that each input value is paired with exactly one output value. This, in turn, allows us to identify the domain and range of the function.
• Analyze how the vertical line test can be used to identify transformations of functions that are still functions.
  • $$The vertical line test is a valuable tool for analyzing transformations of functions. When a function is transformed, such as through translation, reflection, or scaling, the vertical line test can be used to determine if the transformed function is still a function. If a vertical line intersects the transformed graph at only one point for each value of the independent variable, then the transformed function is still a function. This allows us to understand how the properties of the original function, including its domain and range, are affected by the transformation.$$

Related terms

Function:

A function is a relation where each input value is paired with exactly one output value.

Domain:

The domain of a function is the set of all possible input values for the function.

Range:

The range of a function is the set of all possible output values for the function.