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Algebra: functions and linear system

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Part 1
1. Define the word "function."
2. Give an 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.
3. Explain why the example models a function.
4. Give an 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.
5. Explain why your example does not model a function.

Part 2
1. Select any two integers between -12 and +12 which will become solutions to a system of two equations.
2. Write two equations that have your two integers as solutions. Show how using the equations using your integers. Solve the system of equations by the addition/subtraction method. Make sure you the necessary 5 steps are included.

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https://brainmass.com/math/number-theory/algebra-functions-linear-system-563861

Solution Preview

Please see attached.

Part 1
1. A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered ...

Solution Summary

We need to define a function and then give example of a function and a non-function.
in the second part there is a linear system solved by addition/subtraction method.

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17) The demand equation for a certain product is modeled by y = 50-√(0.01x+1) where x is the number of units demanded per day and y is the price per unit.
a) Present a graph of the function.
b) Approximate the demand if the price is $37.55.

18) Consider the function
a) Present a graph of f(x)
b) Solve f(x) = 0
c) Determine where the function is increasing.

19) The average cost per unit for a product for a certain business is given by
C(x) = (0.75x + 5000)/x
a) Present a graph of C
b) Find the average cost per unit when 2000 units are produced.
c) What is the horizontal asymptote?
d) What does the horizontal represent in the context of this problem?

20) Consider the function f(x) = (2x+9)/(4x2-3x).
a) What is the domain of this function?
b) What are the equations for all horizontal and vertical asymptotes?
c) Present a graph of the function.
d) What are the intercepts (both x and y)?

21) Consider the function f(x) = -3x3+20x2-36x+16.
a) Present a graph of the function.
b) Approximate all real roots.

22) Solve the linear system
2x+y = 6
-x+y = 0

23) A small business invests $250000 to produce an item that will sell for $9950. Each unit can be produced for $8650. How many units must be sold to break even?

24) Solve the system of linear equations
2x+ 4y+ z = 1
x- 2y -3z = 2
x+ y - z = -1

25) Given the matrix

A = find

a) A2
b) the inverse of A; that is, (A-1)

26) Given the matrices
A = B =

Find:

a) A+B
b) 4A-3B

27) Solve the system using matrices
x-2y = 1
2x-3y = -2

28) Consider the system of inequalities:

2x+3y≥6
3x-y<15
-x+y≤4
2x+5y≤27

a) Identify all corners of the solution.
b) Minimize the function g = 5x+7y

29) Determine whether each of the following sequences are arithmetic or geometric
a) 7,11,15,19,....
b) 1,5/4,3/2,7/4,...

30) Find the twelfth term of the geometric sequence

5,15,45,...

31) Find the sum of the first fifty terms of the arithmetic sequence

25,35,45,55,65,....

32) Find the sum of the infinite geometric series

∑(0.4)i , where 0≤i<∞

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