12-8

1. Inverse Variation 12-8 Course 3 Warm Up Problem of the Day Lesson Presentation

2. Inverse Variation 12-8 4, 0, 9 1 4 4 Course 3 Warm Up Find f(–4), f(0), and f(3) for each quadratic function. 1.f(x) = x2 + 4 2.f(x) = x2 3.f(x) = 2x2 – x + 3 20, 4, 13 39, 3, 18

3. Inverse Variation 12-8 Course 3 Problem of the Day Use the digits 1–8 to fill in 3 pairs of values in the table of a direct variation function. Use each digit exactly once. The 2 and 3 have already been used. 8 56 1 4 7

4. Inverse Variation 12-8 Course 3 Learn to recognize inverse variation by graphing tables of data.

5. Inverse Variation 12-8 Course 3 Insert Lesson Title Here Vocabulary inverse variation

6. Inverse Variation 12-8 k x 120 x y= y= Course 3 An inverse variation is a relationship in which one variable quantity increases as another variable quantity decreases. The product of the variables is a constant. xy = 120 xy = k

7. Inverse Variation 12-8 The relationship is an inverse variation: y = . 24 x Course 3 Additional Example 1A: Identify Inverse Variation Tell whether the relationship is an inverse variation. A. The table shows how 24 cookies can be divided equally among different numbers of students. 2(12) = 24; 3(8) = 24; 4(6) = 24; 6(4) = 24; 8(3) = 24 xy = 24 The product is always the same.

8. Inverse Variation 12-8 Course 3 Additional Example 1B: Identify Inverse Variation Tell whether each relationship is an inverse variation. B. The table shows the number of cookies that have been baked at different times. The product is not always the same. 12(15) = 180; 24(30) = 720 The relationship is not an inverse variation.

9. Inverse Variation 12-8 The relationship is an inverse variation: y = . 0 x Course 3 Try This: Example 1A Tell whether the relationship is an inverse variation. A. 0(2) = 0; 0(3) = 0; 0(4) = 0; 0(5) = 0; 0(6) = 0 xy = 0 The product is always the same.

10. Inverse Variation 12-8 Course 3 Try This: Example 1B Tell whether the relationship is an inverse variation. B. The product is not always the same. 2(4) = 8; 2(6) = 12 The relationship is not an inverse variation.

11. Inverse Variation 12-8 Graph the inverse variation function. A. f(x) = 4 x 12 12 – Course 3 Additional Example 2A: Graphing Inverse Variations –1 –2 –4 –8 8 4 2 1

12. Inverse Variation 12-8 –1 x 12 12 – 1 3 1 2 – – Course 3 Additional Example 2B: Graphing Inverse Variations Graph the inverse variation function. B. f(x) = 1 3 1 2 1 2 –2 –1

13. Inverse Variation 12-8 4 x 12 12 – Course 3 Try This: Example 2A Graph the inverse variation function. A. f(x) = – 1 2 4 8 –8 –4 –2 –1

14. Inverse Variation 12-8 Graph the inverse variation function. B. f(x) = 8 x Course 3 Try This: Example 2B –1 –2 –4 –8 8 4 2 1

15. Inverse Variation 12-8 1500 x You can see from the table that xy = 5(300) = 1500, so y = . Course 3 Additional Example 3: Application As the pressure on the gas in a balloon changes, the volume of the gas changes. Find the inverse variation function and use it to find the resulting volume when the pressure is 30 lb/in2. If the pressure on the gas is 30 lb/in2, then the volume of the gas will be y = 1500 ÷ 30 = 50 in3.

16. Inverse Variation 12-8 You can see from the table that xy = 10(20) = 200, so y = . 200 x Course 3 Try This: Example 3 An eighth grade class is renting a bus for a field trip. The more students participating, the less each student will have to pay. Find the inverse variation function, and use it to find the amount of money each student will have to pay if 50 students participate. If 50 students go on the field trip, the price per student will be y = 200  50 = $4.

17. Inverse Variation 12-8 Course 3 Insert Lesson Title Here Lesson Quiz: Part 1 Tell whether each relationship is an inverse variation. 1. 2. yes no

18. Inverse Variation 12-8 1 4x Course 3 Insert Lesson Title Here Lesson Quiz: Part 2 3. Graph the inverse variation function f(x) = .