Pre Calculas

Im really struggling and need help with this
1. One of the tables below contains (x,y) values that were generated by a linear function. Determine which table, and then write the equation of the linear function represented by the

Table #1 x 2 5 8 11 14 17 20 y 1 3 7 13 21 31 43

Table #2 x 1 2 3 4 5 6 7 y 10 13 18 21 26 29 34

Table #3 x 2 4 6 8 10 12 14 y 1 6 11 16 21 26 31

2. Give an example of each of the following:

A function whose domain is [2, infinity)
An arithmetic sequence
A system of equations with no solutions

3. For f(x) = 1/x^2-3, find:

f(3)
f(2+h)
4. For f(x) = 1/x-5 and g(x) = x^2+2, find:
1. (fog)(x)
2. (gof)(6)
5. For the sequence given by a (subscript n) = 4n+5 an=4n+5, answer the following:

Find the first five terms
Find the sum of the first 25 terms.
Is this an arithmetic sequence? If so, how can you tell? If not, why not?
6. Graph the area bound by y<1/2x+6, x+3y>=12, x>=0, and x<=12
7. For the function defined by:
f(x)= {x^2, x<=1}
{2x+1, x>1}
a. evaluate f(0)
b. graph f(x)
8. Solve the following system of equations algebraically. Verify your solution either graphically or by using matrices.
3x-y=0
5x+2y=22
9. Solve the following system of equations algebraically. Verify your solution either graphically or by using matrices
8x-2y=5
-12x+3y=7
10.Given matrices A, B, and C below, perform the indicated operations if possible. If the operation is not possible, explain why.
A (3x3) [1st 2, -1, 0] [2nd 0, 5, 0.3] [3rd 1, 4, 10]
B (3x3) [1st 5, 0, 2] [2nd 1, -3, 9] [3rd2, 0, 4]
C (1x1) [1, 3, 5]
1.3A+B
2. B+C
3. CA
11. Given the table below, evaluate the following:

x

-3

-2

-1

0

1

2

3

4

5

f(x)

10

20

30

40

50

60

70

80

90

g(x)

-1

-2

-3

-4

-5

-6

-7

-8

-9

a. (3f+2g(1) b. (fog)(-1)
12. Express the following function, F(x) as a composition of two functions f and g
f(x)= x^2/(x^2+4)
13. You have a coupon for your favorite clothing store for $25 off any purchase of more than $50. The store is also running a 20%-off sale on its entire inventory. Let x be the original price, f(x) be the price with the $25 coupon applied, and g(x) be the price with the 20% discount applied.
a. Write an expression for f(x)
b. Write an expression for g(x)
c. What would the expression (fog)(x) represent?
d. What would the expression (gof)(x) represent?
e. If the store allows you to apply both the 20% discount and the $25-off coupon, does it matter which you apply first? How do you know?

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  1. #1 in a linear function, equal spacing in x produces equal spacing in y. The ratio is called the slope, and is constant. Only table #3 meets that condition.

    #2
    A function whose domain is [2, infinity): √(x-2)
    An arithmetic sequence: 1,2,3,4,...
    A system of equations with no solutions:
    x+y=1
    x+y=2

    #3
    f(x) = 1/(x^2-3), find:
    f(3) = 1/(3^2-3) = 1/6
    f(2+h) = 1/((2+h)^2-3) = 1/(h^2+4h-1)

    #4
    f(x) = 1/x-5 and g(x) = x^2+2, find:
    1. (fog)(x) = f(g(x)) = 1/(g-5) = 1/(x^2+2-5) = 1/(x^2-3)
    2. (gof)(6) = g(f(6)) = g(1) = 1^2+2 = 3

    #5
    an=4n+5, answer the following:
    Find the first five terms: 9,13,17,21,25
    Find the sum of the first 25 terms: (25/2)(2*9+24*4) = 1425
    Is this an arithmetic sequence? Yes, because A_n+1 - A_n = 4(n+1)+5 - (4n+5) = 4, a constant

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  2. Thanks Steve for the help

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