Check 12-5 Homework

1. Check 12-5 Homework

2. Pre-Algebra HOMEWORK Page 637-638 #11-14 & 31-34

3. Students will be able to solve sequences and represent functions by completing the following assignments. • Learn to find terms in an arithmetic sequence. • Learn to find terms in a geometric sequence. • Learn to find patterns in sequences. • Learn to represent functions with tables, graphs, or equations. • Learn to identify linear functions. • Learn to recognize inverse variation by graphing tables of data.

4. Today’s Learning Goal Assignment Learn to recognize inverse variation by graphing tables of data.

5. Inverse Variation 12-8 Warm Up Problem of the Day Lesson Presentation Pre-Algebra

6. Inverse Variation 12-8 4, 0, 9 1 4 4 Pre-Algebra 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

7. 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

8. Vocabulary inverse variation

9. k x 120 x y= y= 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

10. The relationship is an inverse variation: y = . 24 x 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.

11. The relationship is an inverse variation: y = . 0 x 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.

12. 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.

13. 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.

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

15. 4 x 12 12 – Try This: Example 2A Graph the inverse variation function. A. f(x) = – 1 2 4 8 –8 –4 –2 –1

16. –1 x 12 12 – 1 3 1 2 – – Additional Example 2B: Graphing Inverse Variations Graph the inverse variation function. B. f(x) = 1 3 1 2 1 2 –2 –1

17. Graph the inverse variation function. B. f(x) = 8 x Try This: Example 2B –1 –2 –4 –8 8 4 2 1

18. 1500 x You can see from the table that xy = 5(300) = 1500, so y = . 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.

19. You can see from the table that xy = 10(20) = 200, so y = . 200 x 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.

20. Lesson Quiz: Part 1 Tell whether each relationship is an inverse variation. 1. 2. yes no

21. 1 4x Lesson Quiz: Part 2 3. Graph the inverse variation function f(x) = .