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7.11 Variation Functions

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7.11 Variation Functions Mrs. Cassidy it is so weird! The more I study, the worse I do!! Babysitting, my niece earns $12 for 2 hours, $18 for 3 hours. – PowerPoint PPT presentation

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Title: 7.11 Variation Functions


1
7.11 Variation Functions
  • Mrs. Cassidy it is so weird! The more I study,
    the worse I do!!

2
  • Babysitting, my niece earns 12 for
  • 2 hours, 18 for 3 hours.
  • 2 cups 1 pint and 8 cups 4 pints
  • When I walked to high school at a rate of 4 miles
    per hour, it took me half an hour. When
  • I was running late and walked at
  • a rate of 5 miles per hour, it
  • took me 24 minutes.

3
Variation Functions
Direct
Inverse
4
Variation Functions
Direct
Inverse
Constant ? Variable
Constant ?Variable
Lets see what this looks like
5
Direct Variation Functions
  • n gt 0
  • These are called Polynomial functions
  • What did you notice with the graph?
  • As x went up

6
Inverse Variation Functions
  • n lt 0
  • These are called Polynomial functions
  • What did you notice with the graph?
  • As x goes up
  • The x and y axis will act as asymptotes

7
What if no one tells you
  • How do you tell from a graph whether a function
    is a direct variation or inverse variation?
  • How do you tell from a table of values whether a
    function is direct variation or inverse variation?

8
Lets try some
  • Babysitting, my niece earns 12 for 2 hours, 18
    for 3 hours.
  • If x hours and y what she earns, what could
    be an equation?
  • When kickboxing last week, I noticed that it took
    5 lbs of pressure to break a board that was 2
    feet long but only 1 2/3 lbs to break a board
    that is 6 feet long.
  • If x length and y pounds of pressure, what
    could be an equation?

y 6x
9
What if it isnt quite so obvious?
  • There are 3 steps to these types of problems
  • 1. Determine whether it is a direct variation or
    inverse variation problem.
  • 2. Look for patterns (well practice this!)
  • 3. Predict requested value

10
Add-Add Property of Linear Functions
  • Given f(x) 7x, find f(2), f(5) and f(8)
  • For linear functions, adding a constant to x adds
    the constant (not necessarily the same one) to y.

11
Add- Multiply Property of Exponential Functions
  • Given the function f(x) 2(3x), find f(1), f(3)
    and f(5)
  • For exponential functions, adding a constant to x
    multiplies y by a constant.

12
Multiply-Multiply Property of Variation Functions
  • Given the function f(x) 5x2, find f(1), f(2),
    f(4) and f(8)
  • What does it look like you are actually
    multiplying each term by?

13
Multiply-Multiply Property of Variation Functions
  • If y kxn, then multiplying the value of x by
    the constant c multiplies the value of y by the
    constant cn.

14
Multiply-Multiply Property of Variation Functions
  • If y kxn, then multiplying the value of x by
    the constant c multiplies the value of y by the
    constant cn.
  • If , then multiplying the value of
    x by the
  • constant c divides the value of y by the
    constant cn.

15
Practice Phrases
  • y varies directly with x
  • y varies linearly with x
  • y varies inversely with x
  • y is inversely proportional to x
  • y is directly proportional to the cube of x
  • y decreases exponentially with x
  • y increases exponentially with x
  • y varies inversely with the square of x
  • y is a quadratic function of x
  • y is a constant function

16
Lets Practice
  • Example 1
  • In a lightning storm, the time interval between
    the flash and bang is directly proportional to
    the distance between you and the lightning.
  • A) Variables? Which should be independent?
  • b bang d distance distance is
    independent
  • B) If the thunder clap from lightening 5 km away
    takes 15 seconds to reach you, write the
    particular equation.

b5d
17
Lets Practice (cont)
  • C) What is the label on the constant?
  • s/km
  • D) Calculate the times for the thunder sound to
    reach you from lightning bolts which are 1, 2.5
    and 10 km away.
  • 3, 7.5 and 30 seconds

18
Lets Practice more ?
  • Example 2
  • The intensity of radiation received for tumor
    treatment depends on the distance from a source.
    Suppose for that particular source, the intensity
    is 80 mr/hr at 2 meters and 5 mr/hr at 8 meters.
  • A) What is the general equation? What is the
    particular equation?

19
Lets Practice more ?
  • Example 2
  • The intensity of radiation received for tumor
    treatment depends on the distance from a source.
    Suppose for that particular source, the intensity
    is 80 mr/hr at 2 meters and 5 mr/hr at 8 meters.
  • A) What is the general equation? What is the
    particular equation?

20
Lets Practice more ? (cont)
  • C) What would the intensity be if your distance
    were 16 meters? 10 meters? 10 centimeters?
  • D) At what distance would the intensity be 0.5
    meters?
  • 25 meters

1.25
3.2
32,000
21
More? OF course!
  • Truth in Advertising In a claim in an old Time
    Magazine advertisement for South African Airways,
    one Ostrich egg is equivalent to two dozen
    chicken eggs.

22
OK.
  • In your group, come up with the function (make up
    anything you want, within reason ?) and find two
    x/y values.
  • On another piece of paper, write the two sets of
    x/y values down, and then give them to another
    group.

23
Resources
  • http//mathforum.org/library/drmath/view/57504.htm
    l
  • http//www.regentsprep.org/Regents/math/algtrig/AT
    E7/Inverse20Variation.htm
  • http//quiz.uprm.edu/tutorials/direct_var/direct_v
    ar_right.xml
  • Your textbook
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