1. Check 12-5 Homework

2. Pre-Algebra HOMEWORK
Page #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 Warm Up
Pre-Algebra
12-8
Inverse Variation
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
4, 0, 9 4 1 4
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. INVERSE VARIATION Words Numbers Algebra
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.
k x
y =
120 x
y =
xy = 120
xy = k

10. 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.
Number of Students 2 3 4 6 8
Number of Cookies 12
2(12) = 24; 3(8) = 24; 4(6) = 24; 6(4) = 24; 8(3) = 24
xy = 24
The product is always the same.
The relationship is an inverse variation: y = 24 x

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

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.
Number of Students 12 24 36 48 60
Time (min) 15 30 45 75
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. x 2 4 8 1 y 6
The product is not always the same.
2(4) = 8; 2(6) = 12
The relationship is not an inverse variation.

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

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

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

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

18. Volume of Gas by Pressure on Gas
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.
Volume of Gas by Pressure on Gas
Pressure (lb/in2) 5 10 15 20
Volume (in3)
300
150
100 75
You can see from the table that xy = 5(300) = 1500, so y =
1500 x
If the pressure on the gas is 30 lb/in2, then the volume of the gas will be y = 1500 ÷ 30 = 50 in3.

19. Number of Students by Cost per Student
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.
Number of Students by Cost per Student
Students 10 20 25 40
Cost per student 8 5
You can see from the table that xy = 10(20) = 200, so y =
200 x
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. Lesson Quiz: Part 2 1 4x
3. Graph the inverse variation function f(x) =