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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 • Answer: 1st and 4th Functions 200 • Find the domain of the function given below: f x 2x 3 x • Answer: [0,3) 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 hx 2 1 x 324 • Answer: g(x) 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: Ax 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. • Answer: f(x) = 0.12x+5.00 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). • Answer: y = -0.5(x-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? • Answer: 2500 roses 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 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? • Answer: 5 hours 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: Al 3l 300 2l Pieces 100 Which of the following represents the piece- wise function shown below? Answer: c 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 x2 if x 1 • Answer: -2 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 x3 Pieces 500 • The following table gives the Tax Rate Schedule for a person whose filing status was single during the year 2003. Adjusted 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 • Answer: 3910+0.25(x-28400)