Check 12-5 Homework

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Check 12-5 Homework
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Pre-Algebra HOMEWORK

• Page 637-638
• 11-14 31-34

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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.

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Todays Learning Goal Assignment Learn to
recognize inverse variation by graphing tables of
data.
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Inverse Variation
12-8
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
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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
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Problem of the Day Use the digits 18 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.
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56
1
4
7
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Vocabulary
inverse variation
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INVERSE VARIATION 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.
xy 120
xy k
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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 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.
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Try This Example 1A
Tell whether the relationship is an inverse
variation. A.
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 product is always the same.
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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 60 75
The product is not always the same.
12(15) 180 24(30) 720
The relationship is not an inverse variation.
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Try This Example 1B
Tell whether the relationship is an inverse
variation. B.
x 2 4 8 1 2
y 4 2 1 8 6
The product is not always the same.
2(4) 8 2(6) 12
The relationship is not an inverse variation.
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Additional Example 2A Graphing Inverse Variations
x y
4
2
1


1
2
4
1
2
4
8
8
4
2
1
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Try This Example 2A
Graph the inverse variation function. A. f(x)
x y
4
2
1


1
2
4
1
2
4
8
8
4
2
1
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Additional Example 2B Graphing Inverse Variations
Graph the inverse variation function. B. f(x)
x y
3
2
1


1
2
3
1 3
1 2
1
2
2
1
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Try This Example 2B
x y
8
4
2
1
1
2
4
8
1
2
4
8
8
4
2
1
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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 Volume of Gas by Pressure on Gas Volume of Gas by Pressure on Gas Volume of Gas by Pressure on Gas Volume of Gas by Pressure on Gas
Pressure (lb/in2) 5 10 15 20
Volume (in3) 300 150 100 75
If the pressure on the gas is 30 lb/in2, then the
volume of the gas will be y 1500 30 50 in3.
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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 Number of Students by Cost per Student Number of Students by Cost per Student Number of Students by Cost per Student Number of Students by Cost per Student
Students 10 20 25 40
Cost per student 20 10 8 5
If 50 students go on the field trip, the price
per student will be y 200 ? 50 4.
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Lesson Quiz Part 1
Tell whether each relationship is an inverse
variation. 1. 2.
yes
no
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Lesson Quiz Part 2
3. Graph the inverse variation function f(x)
.