Representing Inverse Fucntions through tables and graphs

Hope this can help

1. Lesson 2 Representing Inverse Functions through Tables and Graphs

2. At the end of this lesson, the learner should be able to correctly determine whether a function is one-to-one through the use of the horizontal line test ; and correctly represent the inverse of a function using graph and table of values .

3. How can you perform the horizontal line test ? How can you represent the inverse of a function using table of values and graph ?

4. Before we discuss thoroughly how to represent an inverse function using table of values and graph, let us observe how the graphs of a function and its inverse are related by using an applet. (Click the link to access the applet.) Boyadzhiev , Irina. “Inverse Function.” Geogebra. Retrieved 21 March 2019 from https://www.geogebra.org/m/BXGpVsKJ .

5. How is the graph of a function related to the graph of its inverse? How can you represent the inverse of a function when its graph is given? Given the graph of a function, how can you draw the graph of its inverse?

6. Representing Inverse Functions through Table of Values We can interchange the - and -coordinates in a table of values of a function to come up with a table of values for its inverse function.   1 Example: Consider the function . This function has the following table of values.  

7. By interchanging the - and -coordinates of each ordered pair, we get the following table of values for the inverse function of .  

8. Example: Using the table of values for and its inverse, we can draw its graph.   Representing Inverse Functions using Graphs We can draw the graph of an inverse function by plotting the points from its table of values. 2

9. Example: The graph on the right represents a one-to-one function since if we draw a horizontal line anywhere on the graph, it intersects the graph at only one point. Horizontal Line Test If any horizontal line drawn anywhere on the graph intersects the graph exactly once, then the graph is one-to-one. Otherwise, it is not one-to-one. 3

10. Example: The graph on the right does not represent a one-to-one function since we can find a horizontal line that intersects the graph more than once. Thus, the function represented by this graph does not have an inverse function.

11. Example 1 : Determine whether the function represented by the given graph has an inverse function by performing the horizontal line test.

12. Solution: If we draw a horizontal line on the graph as illustrated, it intersects the graph more than once. It follows that the function represented by this graph is not one-to-one and does not have an inverse function.

13. Example 2 : Sketch the graph of given the graph of the function .  

14. Solution : The graph passes through the ordered pairs , , , and . We can put these points in a table of values.  

15. Solution : By interchanging the - and -coordinates of each ordered pair, we get a table of values for as shown below.  

16. Solution : We can now plot the points from this table of values and then connect these points using a smooth curve.

17. Individual Practice: Perform the horizontal line test to determine whether the function represented by the given graph is one-to-one.

18. Individual Practice: Draw the graph of the function represented by following table of values by connecting the points using a smooth curve. Then, draw the graph of its inverse.

19. Group Practice : To de done in groups of four. Find the inverse of . Then, draw its graph and the graph of its inverse.  

20. Representing Inverse Functions through Table of Values We can interchange the - and -coordinates in a table of values of a function to come up with a table of values for its inverse function.   1 Representing Inverse Functions using Graphs We can draw the graph of an inverse function by plotting the points from its table of values. 2 Horizontal Line Test If any horizontal line drawn anywhere on the graph intersects the graph exactly once, then the graph is one-to-one. Otherwise, it is not one-to-one. 3

21. How do you represent an inverse function using graph or table values? In what real-life context can you relate the concept of inverse function? How can you use the graph of a function to graph its inverse ?