1. Inverse Variation 13-7 Warm Up Problem of the Day Lesson Presentation
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. Inverse Variation 13-7 Warm Up
Course 3
13-7
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

3. Inverse Variation 13-7 Problem of the Day
Course 3
13-7
Inverse Variation
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. Course 3
13-7
Inverse Variation
Learn to recognize inverse variation by graphing tables of data.

5. Insert Lesson Title Here
Course 3
13-7
Inverse Variation
Insert Lesson Title Here
Vocabulary
inverse variation

6. Inverse Variation INVERSE VARIATION 13-7 Words Numbers Algebra
Course 3
13-7
Inverse Variation
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

7. Additional Example 1A: Identify Inverse Variation
Course 3
13-7
Inverse Variation
Additional Example 1A: Identify Inverse Variation
Determine whether the relationship is an inverse variation.
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

8. Inverse Variation 13-7 Helpful Hint
Course 3
13-7
Inverse Variation
To determine if a relationship is an inverse variation, check if the product of x and y is always the same number.
Helpful Hint

9. Additional Example 1B: Identify Inverse Variation
Course 3
13-7
Inverse Variation
Additional Example 1B: Identify Inverse Variation
Determine whether each relationship is an inverse variation.
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.

10. Inverse Variation 13-7 Check It Out: Example 1A
Course 3
13-7
Inverse Variation
Check It Out: Example 1A
Determine whether the relationship is an inverse variation. x 30 20 15 12 10 y 2 3 4 5 6
30(2) = 60; 20(3) = 60; 15(4) = 60; 12(5) = 60; 10(6) = 60
xy = 60
The product is always the same.
The relationship is an inverse variation: y = 60 x

11. Inverse Variation 13-7 Check It Out: Example 1B
Course 3
13-7
Inverse Variation
Check It Out: Example 1B
Determine whether the relationship is an inverse variation. 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.

12. Additional Example 2A: Graphing Inverse Variations
Course 3
13-7
Inverse Variation
Additional Example 2A: Graphing Inverse Variations
Create a table. Then graph the inverse variation function.
f(x) = 4 x x y –4 –2 –1 1 2 4 –1 –2 –4 – 12 –8 12 8 4 2 1

13. Additional Example 2B: Graphing Inverse Variations
Course 3
13-7
Inverse Variation
Additional Example 2B: Graphing Inverse Variations
Create a table. Then graph the inverse variation function.
f(x) = x y –3 –2 –1 1 2 3 –1 x
1 3
1 2 1 – 12 2 12 –2 –1
1 2 –
1 3 –

14. Inverse Variation 13-7 Check It Out: Example 2A
Course 3
13-7
Inverse Variation
Check It Out: Example 2A
Create a table. Then graph the inverse variation function.
f(x) = – 4 x x y –4 –2 –1 1 2 4 1 2 4 – 12 8 12 –8 –4 –2 –1

15. Inverse Variation 13-7 Check It Out: Example 2B
Course 3
13-7
Inverse Variation
Check It Out: Example 2B
Create a table. Then graph the inverse variation function.
f(x) = 8 x x y –8 –4 –2 –1 1 2 4 8 –1 –2 –4 –8 8 4 2 1

16. Volume of Gas by Pressure on Gas
Course 3
13-7
Inverse Variation
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.

17. Number of Students by Cost per Student
Course 3
13-7
Inverse Variation
Check It Out: 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.

18. Insert Lesson Title Here
Course 3
13-7
Inverse Variation
Insert Lesson Title Here
Lesson Quiz: Part I
Tell whether each relationship is an inverse variation. 1. 2.
yes no

19. Insert Lesson Title Here
Course 3
13-7
Inverse Variation
Insert Lesson Title Here
Lesson Quiz: Part II 1 4x
3. Graph the inverse variation function f(x) =