# Final Exam Review Part 1 by gabyion

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```									MATH 110

Review
Jeopardy
Functions   Straight as     Word     Pieces
an arrow     Problems
100           100          100      100

200          200          200       200

300          300          300       300

400          400          400       400

500          500          500       500
Final Jeopardy?
•   Final Exam:
•   Monday May 9th, 2005
•   8:00am to 10:00am
•   Room PAS 201
•   Get to the exam no later than 7:45am
Functions 100
• Which of the tables express y as a function of x?
x      -2       0     -1     0      4
y      5        1      3     1      5

x      2        -2    0      2      4
y      5        4     3      2      1

x      1        2     1      4      5
y      0        3     -2     1      9

x      1        2     -3     4      6
y      3        1      3     -1     5

Functions 200
• Find the domain of the function given
below:

f x  
2x
3 x
Functions 300
• The graphs of f(x) and g(x) are shown.

y                                                              y



                                                              








x                                                                      x

                                                                                     








                                                             





f(x)                                                           g(x)

• Find the domain and range of each function
• Answer: f(x) D: [-3,infinity) R: [-4,infinity)
g(x) D: [-5,5] R: [-3,3]
Functions 400
• Which of the functions shown has a domain of
all real numbers except 18?

f  x   x  18

g x  
2x
x  18
hx   2
1
x  324
Functions 500
• A 24 inch wire is cut into 4 pieces to form
a rectangle whose shortest side has a
length of x. Express the area of this
rectangle as a function of x. What is the
domain of this function?

• Answer: Ax   x 12  x ; D : (0,12 )
Straight as an Arrow 100
• Suppose that the quantity sold, q, of a
particular product can be expressed as a
linear function of the product’s price, p, by
the linear function q(p) = -50p + 2000.
Determine the slope of the graph of q(p)
and interpret the slope in practical terms.
• Answer: slope is -50; this means that the
amount sold decreases by 50 when the
product’s price increase by \$1.00.
Straight as an arrow 200
• Find the coordinates of the x and y
intercepts of 3x + 7y -1 =0.

• Answer: x-int (1/3,0) ; y-int (0, 1/7)
Straight as an arrow 300
• A small electrical co-op in rural Arizona
charges its customers a \$5.00 basic
monthly fee plus \$0.12 per kilowatt hour
used. Write a function to represent the
monthly charge in dollars on an electric bill
in terms of the number of kilowatt hours
used.
Straight as an arrow 400
• Determine whether the following table is a
linear function. If it is find the equation of
the line.
x     1      2      3      4     5
y     3     5.1    7.2    9.3   11.4

• Answer: yes constant rate of change;
equation y = 2.1x +0.9
Straight as an arrow 500
• Find the equation of the line perpendicular
to 2x – y = 3 which passes through the
point (1,3).

Word Problems 100
• A couple invests \$3500 to build a rose
garden. On average, it costs them \$0.35
to grow each rose. If each rose can be
sold for \$1.75, how many roses must be
sold to break even?

Word Problems 200
• A shop owner wants to mix high quality
coffee beans that cost \$5.00 per pound
with cheap, crummy tasting beans that
cost \$1.00 per pound to get 20 pounds of
a blend which should be worth \$3.50 per
pound. How much of the cheap blend
should be used?

Word Problems 300
• You invest \$1000 in two accounts. The
first pays 6% annual interest, the other
pays 9% annual interest. At the end of
one year you collect \$84.60 in interest.
How much was invested in each account?

• Answer: \$180 in the 6% account and
\$820 in the 9% account.
Word Problems 400
• A train that is traveling 52 mph leaves the
station and goes west. Another train
leaves the station on a parallel track 1
hour later traveling west at 65 mph. How
long until the fast train catches up with the
slow train?

Word Problems 500
• A rancher wishes to enclose two adjacent rectangular
corrals such that the right-hand corral has twice the
length of the left hand (see diagram). She has 900 feet
of fencing. Express the area of the enclosure as function
of the length.      Answer: Al   3l 300  2l 
Pieces 100
Which of the following represents the piece-
wise function shown below?
Pieces 200
• Sketch the graph of the piece-wise defined
function shown below:
 x  1 if                    x 1
f x   
  2 x if                    x 1
y












x

                                              













Pieces 300
• Find g(0) for the function given below:

2 x 2  4 x if   x 1
g x   
 x2        if   x 1

Pieces 400
• Write the piece-wise function for the graph
shown:

• Answer:             2.5 x  5.5
 4
if    3  x  1
f x    x  2   1 if   1  x  2
 3
 2x  5        if    2 x3
Pieces 500
• The following table gives the Tax Rate Schedule for a person whose
filing status was single during the year 2003.
gross                                 of the
income is    but not                  amount
over         over     Tax Due         over . . .
\$0       7,000       10%             \$0
\$7,000     28,400  \$700.00+15%      \$7,000
\$28,400     68,800  \$3910.00+25%    \$28,400
\$68,800    143,500 \$14010.00+28%    \$68,800
\$143,500    311,950 \$34926.00+33%   \$143,500
\$311,950            \$90514.50+35%   \$311,950

• Determine a formula for the tax a person would pay with an adjusted
gross income that is between \$28,400 and \$68,800