1. Splash Screen

2. Concept

3. Find an Inverse Relation
GEOMETRY The ordered pairs of the relation {(1, 3), (6, 3), (6, 0), (1, 0)} are the coordinates of the vertices of a rectangle. Find the inverse of this relation. Describe the graph of the inverse.
To find the inverse of this relation, reverse the coordinates of the ordered pairs. The inverse of the relation is {(3, 1), (3, 6), (0, 6), (0, 1)}.
Example 1

4. Find an Inverse Relation
Answer: Plotting the points shows that the ordered pairs also describe the vertices of a rectangle. Notice that the graph of the relation and the inverse are reflections over the graph of y = x.
Example 1

5. GEOMETRY The ordered pairs of the relation {(–3, 4), (–1, 5), (2, 3), (1, 1), (–2, 1)} are the coordinates of the vertices of a pentagon. What is the inverse of this relation?
A. cannot be determined
B. {(–3, 4), (–1, 5), (2, 3), (1, –2)}
C. {(–3, 4), (–1, 5), (2, 3), (1, 1), (–2, 1)}
D. {(4, –3), (5, –1), (3, 2), (1, 1), (1, –2)}
Example 1

6. Concept

7. Then graph the function and its inverse.
Find and Graph an Inverse
Then graph the function and its inverse.
Step 1 Replace f(x) with y in the original equation.
Step 2 Interchange x and y.
Example 2

8. Step 4 Replace y with f –1(x). y = –2x + 2  f –1(x) = –2x + 2
Find and Graph an Inverse
Step 3 Solve for y.
Inverse
Multiply each side by –2.
Add 2 to each side.
Step 4 Replace y with f –1(x).
y = –2x + 2  f –1(x) = –2x + 2
Example 2

9. Find and Graph an Inverse
Example 2

10. Find and Graph an Inverse
Answer:
Example 2

11. Graph the function and its inverse.B. C. D.
Example 2

12. Concept

13. Verify that Two Functions are Inverses
Check to see if the compositions of f(x) and g(x) are identity functions.
Example 3

14. Verify that Two Functions are Inverses
Answer: The functions are inverses since both [f ○ g](x) and [g ○ f](x) equal x.
Example 3

15. A. They are not inverses since [f ○ g](x) = x + 1.
B. They are not inverses since both compositions equal x.
C. They are inverses since both compositions equal x.
D. They are inverses since both compositions equal x + 1.
Example 3

16. Homework: p. 396 # 3 – 39 (x3)

17. End of the Lesson