Math 110 (Lehmann) Lecture 1.2 Scattergrams, Marijuana and Inventions.
MATH 110
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Transcript of MATH 110
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MATH 110
Review
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Jeopardy
Functions Straight as an arrow
Word Problems
Pieces
100 100 100 100
200 200 200 200
300 300 300 300
400 400 400 400
500 500 500 500
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Final Jeopardy?
• Final Exam:
• Monday December 12th, 2005
• 8:00am to 10:00am
• Room S SCI 100
• Get to the exam no later than 7:30am
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Functions 100• Which of the tables express y as a function of x?
• Answer: 1st and 4th
x -2 0 -1 0 4y 5 1 3 1 5
x 2 -2 0 2 4y 5 4 3 2 1
x 1 2 1 4 5y 0 3 -2 1 9
x 1 2 -3 4 6y 3 1 3 -1 5
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Functions 200
• Find the domain of the function given below:
• Answer: [0,3)
x
xxf
3
2
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Functions 300• The graphs of f(x) and g(x) are shown.
• 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]
x
y
x
y
f(x) g(x)
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Functions 400
• Which of the functions shown has a domain of all real numbers except 18?
• Answer: g(x)
324
118
2
18
2
xxh
x
xxg
xxf
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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: )12,0(:;12 DxxxA
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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.
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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)
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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.
• Answer: f(x) = 0.12x+5.00
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Straight as an arrow 400
• Determine whether the following table is a linear function. If it is find the equation of the line.
• Answer: yes constant rate of change; equation y = 2.1x +0.9
x 1 2 3 4 5y 3 5.1 7.2 9.3 11.4
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Straight as an arrow 500
• Find the equation of the line perpendicular to 2x – y = 3 which passes through the point (1,3).
• Answer: y = -0.5(x-1)+3
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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?
• Answer: 2500 roses
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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?
• Answer: 7.5 pounds
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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.
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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?
• Answer: 5 hours
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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: lllA 23003
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Pieces 100Which of the following represents the piece-
wise function shown below?
Answer: c
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Pieces 200• Sketch the graph of the piece-wise defined
function shown below:
12
11
xifx
xifxxf
x
y
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Pieces 300
• Find g(0) for the function given below:
• Answer: -2
12
142 2
xifx
xifxxxg
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Pieces 400
• Write the piece-wise function for the graph shown:
• Answer:
3252
21123
4135.55.2
xifx
xifx
xifx
xf
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Pieces 500• The following table gives the Tax Rate Schedule for a person whose
filing status was single during the year 2003.
• Determine a formula for the tax a person would pay with an adjusted gross income that is between $28,400 and $68,800
• Answer: 3910+0.25(x-28400)
Adjusted gross income is over
but not over Tax Due
of the amount 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