check 12-5 homework
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Check 12-5 Homework. Pre-Algebra HOMEWORK. Page 637-638 #11-14 & 31-34. 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 . - PowerPoint PPT PresentationTRANSCRIPT
Pre-Algebra
12-8 Inverse Variation
Check 12-5 Homework
Pre-Algebra
12-8 Inverse Variation
Pre-Algebra HOMEWORK
Page 637-638
#11-14 & 31-34
Pre-Algebra
12-8 Inverse Variation
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.
Pre-Algebra
12-8 Inverse Variation
Today’s Learning Goal Assignment
Learn to recognize inverse variation by graphing tables of data.
Pre-Algebra
12-8 Inverse Variation12-8 Inverse Variation
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
12-8 Inverse Variation
Warm UpFind 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
Pre-Algebra
12-8 Inverse Variation
14
4, 0, 94
Pre-Algebra
12-8 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
1 4
56
7
Pre-Algebra
12-8 Inverse Variation
Vocabulary
inverse variation
Pre-Algebra
12-8 Inverse Variation
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
k x
y =120 x
y =
INVERSE VARIATIONINVERSE VARIATION
Words Numbers Algebra
Pre-Algebra
12-8 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.
Additional Example 1A: Identify Inverse Variation
Number of Students 2 3 4 6 8
Number of Cookies 12 8 6 4 3
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 = .24x
Pre-Algebra
12-8 Inverse Variation
Tell whether the relationship is an inverse variation.
A.
Try This: Example 1A
x 0 0 0 0 0
y 2 3 4 5 6
0(2) = 0; 0(3) = 0; 0(4) = 0; 0(5) = 0; 0(6) = 0
xy = 0
The relationship is an inverse variation: y = . 0x
The product is always the same.
Pre-Algebra
12-8 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.
Additional Example 1B: Identify Inverse Variation
Number of Students 12 24 36 48 60
Time (min) 15 30 45 60 75
12(15) = 180; 24(30) = 720
The relationship is not an inverse variation.
The product is not always the same.
Pre-Algebra
12-8 Inverse Variation
Tell whether the relationship is an inverse variation.
B.
Try This: Example 1B
x 2 4 8 1 2
y 4 2 1 8 6
2(4) = 8; 2(6) = 12
The relationship is not an inverse variation.
The product is not always the same.
Pre-Algebra
12-8 Inverse VariationAdditional Example 2A: Graphing Inverse Variations
Graph the inverse variation function.
A. f(x) = 4x x y
–4
–2
–1
1
2
4
–1212
–1
–2
–4
–8
8
4
2
1
Pre-Algebra
12-8 Inverse Variation
Try This: Example 2A
x y
–4
–2
–1
1
2
4
–1212
1
2
4
8
–8
–4
–2
–1
Graph the inverse variation function.
A. f(x) = – 4x
Pre-Algebra
12-8 Inverse Variation
Graph the inverse variation function.
B. f(x) =
Additional Example 2B: Graphing Inverse Variations
–1 x
x y
–3
–2
–1
1
2
3
–1212
1 31 21
2
–2
–11 2
–
1 3
–
Pre-Algebra
12-8 Inverse Variation
Try This: Example 2B
Graph the inverse variation function.
B. f(x) = 8x x y
–8
–4
–2
–1
1
2
4
8
–1
–2
–4
–8
8
4
2
1
Pre-Algebra
12-8 Inverse Variation
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.
Additional Example 3: Application
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
xIf the pressure on the gas is 30 lb/in2, then the volume of the gas will be y = 1500 ÷ 30 = 50 in3.
Pre-Algebra
12-8 Inverse VariationTry 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 20 10 8 5
You can see from the table that xy = 10(20) = 200, so y = . 200
xIf 50 students go on the field trip, the price per student will be y = 200 50 = $4.
Pre-Algebra
12-8 Inverse Variation
Tell whether each relationship is an inverse variation.
1.
2.
Lesson Quiz: Part 1
no
yes
Pre-Algebra
12-8 Inverse Variation
Lesson Quiz: Part 2
3. Graph the inverse variation function f(x) = .14x