1. Holt Algebra 2 7-2 Inverses of Relations and Functions Graph and recognize inverses of relations and functions. Find inverses of functions. Objectives

2. Holt Algebra 2 7-2 Inverses of Relations and Functions NOTES: 1.A relation consists of the following points and the segments drawn between them. Write the ordered pairs for the inverse. Graph both. And, find the domain and range of the inverse relation: x0347 y27610 2. Graph f(x) = 3x – 4. Then write and graph the inverse. 3. A thermometer gives a reading of 25° C. Use the formula C = 5/9(F – 32). Write the inverse function and use it to find the equivalent temperature in °F.

3. Holt Algebra 2 7-2 Inverses of Relations and Functions You can also find and apply inverses to relations and functions. To graph the inverse relation, you can reflect each point across the line y = x. This is equivalent to switching the x- and y- values in each ordered pair of the relation. A relation is a set of ordered pairs. A function is a relation in which each x-value has, at most, one y-value paired with it. Remember!

4. Holt Algebra 2 7-2 Inverses of Relations and Functions Graph the relation and connect the points. Then graph the inverse. Identify the domain and range of each relation. Example 1: Graphing Inverse Relations x 0158 y 2569 Graph each ordered pair and connect them. x 2569 y 0158 ● ● ● ● Switch the x- and y-values in each ordered pair.

5. Holt Algebra 2 7-2 Inverses of Relations and Functions Example 1 Continued Reflect each point across y = x, and connect them. Make sure the points match those in the table. Domain:{x|0 ≤ x ≤ 8} Range :{y|2 ≤ x ≤ 9} Domain:{x|2 ≤ x ≤ 9} Range :{y|0 ≤ x ≤ 8}

6. Holt Algebra 2 7-2 Inverses of Relations and Functions Use inverse operations to write the inverse of f(x) = 3(x – 7). The variable x is subtracted by 7, then is multiplied by 3. First, undo the multiplication by dividing by 3. Then, undo the subtraction by adding 7. Example 2: Writing Inverses of Multi-Step Functions 1 3 f –1 (x) = x + 7

7. Holt Algebra 2 7-2 Inverses of Relations and Functions You can also find the inverse function by writing the original function with x and y switched and then solving for y. In a real-world situation, don’t switch the variables, because they are named for specific quantities. Remember!

8. Holt Algebra 2 7-2 Inverses of Relations and Functions Example 3: Writing and Graphing Inverse Functions Switch x and y. Solve for y. Set y = f(x) and graph f. Graph f(x) = – x – 5. Then write the inverse and graph both on the same graph. 1 2 1 2 y = – x – 5 1 2 x = – y – 5x + 5 = – y 1 2 –2x – 10 = y Write in y = format. y = –2(x + 5)

9. Holt Algebra 2 7-2 Inverses of Relations and Functions Example 3 Continued f –1 (x) = –2x – 10 f f –1

10. Holt Algebra 2 7-2 Inverses of Relations and Functions NOTES: Part I 1. A relation consists of the following points and the segments drawn between them. Write the ordered pairs for the inverse. Graph both. And, find the domain and range of the inverse relation: x0347 y27610

11. Holt Algebra 2 7-2 Inverses of Relations and Functions Notes: Part II 2. Graph f(x) = 3x – 4. Then write and graph the inverse. f –1 (x) = x + 1 3 4 3 f f –1

12. Holt Algebra 2 7-2 Inverses of Relations and Functions Notes: Part III 3. A thermometer gives a reading of 25° C. Use the formula C = (F – 32). Write the inverse function and use it to find the equivalent temperature in °F. 5 9 F = C + 32; 77° F 9 5