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Function











































Part 1
In your own words, define the word “function.”
Give your own example of a function using a set of at least 4 ordered pairs. The domain will be any four integers between 0 and +10. The range will be any four integers between -12 and 5. Your example should not be the same as those of other students or the textbook. There are thousands of possible examples.
Explain why your example models a function. This is extremely important for your learning.
Give your own example of at least four ordered pairs that does not model a function. The domain will be any four integers between 0 and +10. The range will be any four integers between -12 and +5. Your example should not be the same as those of other students or the textbook. There are thousands of possible examples.
Explain why your example does not model a function.
Part 2
Select any two integers between -12 and +12 which will become solutions to a system of two equations.
Write two equations that have your two integers as solutions. Show how you built the equations using your integers. Your solution and equations should not be the same as those of other students or the textbook. There are infinite possibilities.
Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps. Use the example on page 357 of Mathematics in Our World as a guide.
Respond to at least two of your classmates’ postings. Do you agree or disagree that their examples model functions? Follow their 5 steps. Do their calculations follow the correct rules of algebra?

Comments for Function

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Apr 12, 2011
Function - Definition
by: Staff

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Section B


Functions have three characteristics:


(1) There can be any number of independent variables (these are the input variables: x, z, q, r, etc.)

For example: f(x,z,r,q) = x + z + r + q

(2) There can be only one dependent variable.

For example: f(x,z,r,q) is the only dependent variable in the example under 1.

(3) The dependent variable can only be equal to a single value at a time.

For example:

f(x) = x² is a function because f(x) has only one unique value for every value of x.


y = 5 + sqrt(-x) is NOT a FUNCTION because y has two values for every x (where x ≤ 0). [y = 5 + sqrt(-x) is the equation for a parabola on its side: a horizontal parabola.]



EXAMPLE OF A FUNCTION using 4 ordered pairs


(x,y)

(0,2)
(1,3)
(2,4)
(3,5)


WHY this EXAMPLE IS A FUNCTION

The example is a function because the y coordinate has only a single, unique value for every value of x.


EXAMPLE of ordered pairs which is NOT A FUNCTION


(x,y)

(0,2)
(1,3)
(2,5)
(2,6)


WHY this EXAMPLE is NOT A FUNCTION

The example is NOT a function because the y coordinate has 2 values at the same time (5 & 6) when x = 2.


Part 2

SELECT TWO INTEGERS between -12 and +12 which will become solutions to a system of two equations.

x = 0 and y = 5


WRITE TWO EQUATIONS

Integers: x = 0 and y = 5 are the solutions to the following two equations

x + y = 5

3x + 2y = 10


HOW the EQUATIONS WERE BUILT

Once the integers were selected, I used the integers to complete an arbitrary calculation which was made up on the spot.

x = 0, and y = 5

0 + 5 = 5
x + y = 5

3*0 + 2*5 = 10
3x + 2y = 10


SOLVE YOUR SYSTEM OF EQUATIONS by the addition/subtraction method

x + y = 5

3x + 2y = 10

Multiply each side of the equation no.1 by -2

(-2)*(x + y) = (-2)*5

-2x - 2y = -10

Add this equation to equation no. 2

-2x - 2y = -10
3x + 2y = 10
-------------------
-2x - 2y + 3x + 2y = -10 + 10

-2x + 3x - 2y + 2y = -10 + 10

x + 0 = 0

x = 0

Substitute 0 for x in equation no. 1, and then solve for y

x + y = 5

0 + y = 5

y = 5





Thanks for writing.


Staff
www.solving-math-problems.com


Apr 12, 2011
Function - Definition
by: Staff


Section A

The question:

Part 1

In your own words, define the word “function.”
Give your own example of a function using a set of at least 4 ordered pairs. The domain will be any four integers between 0 and +10. The range will be any four integers between -12 and 5. Your example should not be the same as those of other students or the textbook. There are thousands of possible examples.
Explain why your example models a function. This is extremely important for your learning.
Give your own example of at least four ordered pairs that does not model a function. The domain will be any four integers between 0 and +10. The range will be any four integers between -12 and +5. Your example should not be the same as those of other students or the textbook. There are thousands of possible examples.
Explain why your example does not model a function.

Part 2

Select any two integers between -12 and +12 which will become solutions to a system of two equations.
Write two equations that have your two integers as solutions. Show how you built the equations using your integers. Your solution and equations should not be the same as those of other students or the textbook. There are infinite possibilities.
Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps. Use the example on page 357 of Mathematics in Our World as a guide.
Respond to at least two of your classmates’ postings. Do you agree or disagree that their examples model functions? Follow their 5 steps. Do their calculations follow the correct rules of algebra?


The answer:

Part 1

DEFINE A FUNCTION

A function is a mathematical statement which shows how one quantity is related to, and dependent upon, at least one other quantity.

For example, what you earn on a job is RELATED TO and completely DEPENDENT upon two things: the rate of pay and the number of hours worked.

Total Pay = (rate of pay)*(number of hours worked)

Total Pay is a function of two variables: rate of pay & hours worked

T(p,h) = p*h

or

f(p,h) = p*h


Note that an equation and a function are not the same, although an equation can often be rewritten as a function.

An equation is always equal to a specific value on each side of the equal sign. Here are some examples of equations:

x + 3 = 9x

x + y = 130

x³ + x² = 0



The second equation listed in the three examples can be rewritten as a function

x + y = 130 is an equation

y = 130 - x is a function

f(x) = 130 - x is the same function

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