Exam 1 Review Sp16 O Brien. Exam 1 Review:
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1 Exam Review:..6 Directions: Try to work the following problems with your book, notes, and homework closed. You may have your graphing calculator and some blank paper. The idea is to practice working problems with no resources other than what you will have during the exam. This is will help you to identify your weak areas where you need further study. If you miss a problem, practice working some problems like it with your book, notes, and homework open. Then work a few similar problems with your resources closed. Get in the habit of showing all of your support work on every problem.. Find the length of the unknown side of the right triangle. a and b represent the lengths of the legs and c represents the length of the hypotenuse. b = 7, c = ; find a..8. Find a) the distance between P and Q and b) the midpoint of the line segment joining P and Q. P(8.9,.6), Q(.9,.6)..9. Determine the domain D and range R of the given relation and tell whether it is a function...6. Use the graph of y = f(x) to find each function value: a) f( ) b) f(0) c) f() d) f()...76 f x =... Give the a) x-intercept, b) y-intercept, c) domain, d) range, e) slope of the line. Do not use a calculator.. Graph the linear function: ( ) x 6. By noon, inches of rain had fallen during a storm. Rain continued to fall at a rate of inch per hour. a. Find a formula for a linear function f that models the amount of rainfall x hours past noon. b. Find the total amount of rainfall by :0 p.m Find the slope-intercept form of the equation of the line through (, 6.) and (,.). Do not use a calculator Graph the line x y = 9 by hand. Give the x- and y-intercepts...
2 9. Write the equation of the line satisfying the given conditions, giving it in slope-intercept form, if possible. a) Through (, 0), perpendicular to 8x y = 7..6 b) Through (, 8), parallel to y =.x A person is riding a bicycle along a straight highway. The graph at the right shows the rider s distance y in miles from an interstate highway after x hours. a) Find the slope-intercept form of the line. b) How fast is the biker traveling? c) How far was the biker from the interstate highway initially? d) How far was the biker from the interstate highway after hour and minutes?..6. Worldwide gambling revenue from online betting was $8 billion in 007 and $ billion in 00. a) Write the equation of a line y= mx + b that models this information, where y is in billions of dollars and x is the year. b) Use this equation to estimate online betting revenue in The following table lists the average tuition and fees(in constant 00 dollars) at public colleges and universities for selected years...70 Year Tuition & Fees ,86,97 a) Use regression to find a formula f(x) = mx + b so that f models the data. b) Use the model to predict tuition and fees in 06.. Find the zero of the function f. Do not use a calculator. f(x) =.x + (x ) +.(x + 9)..9. Solve the following equation analytically x = x. Classify the following equation as a contradiction, an identity, or a conditional equation. Give the solution set...7 [6 ( + x)] = + x 6. Solve the following inequality analytically. Write the solution set in interval notation...9 x + x x + 7 < Use algebra to solve the following applications, not just trial and error or common sense. 7. The length of a rectangular mailing label is cm less than twice the width. The perimeter is cm. Find its dimensions..6.0
3 8. At :00 p.m. a runner heads north on a highway, jogging at 0 mph. At :0 p.m. a driver heads north on the same highway to pick up the runner. If the car travels at mph, how long will it take the driver to catch the runner? How many gallons of a % acid solution must be mixed with gallons of a 0% solution to obtain a 7% solution? A baker makes cakes and sells them at county fairs. Her initial cost for the Benton County Fair was $0.00. She figures each cake cost $.0 to make and she charges $6.0 per cake. Let x represent the number of cakes sold and assume no cakes are leftover. a) Express the total cost C as a function of x. b) Express the revenue R as a function of x. c) Determine analytically the value of x for which revenue equals cost Nancy B. Kindy won $00,000 in a state lottery. She first paid income tax of 0% on the winnings. Of the rest, she invested some at.% and some at %, earning $0 interest per year. How much did she invest at each rate? Solve the formula for the specified variable..6.6 P = L + W for W. Determine the largest open intervals of the domain over which each function is..8 a) increasing; b) decreasing; and c) constant. Then give the d) domain; and e) range.. Write the equation that results in the desired translation. Do not use a calculator. The squaring function, shifted 000 units to the left and units downward.... Without a graphing calculator, determine the domain and range of the following function. f(x) = (x ) Use translations of one of the basic functions to sketch the graph of y = x +. Do not use a calculator Write the equation that results in the desired transformations. Do not use a calculator. The square root function, vertically shrunk by applying a factor of. and reflected across the x-axis Describe the series of transformations applied to y = x that would result in the graph of..9 y = x +. Be specific about direction and magnitude. [Note the change in directions.]
4 9. Give the equation of the function whose graph is described below...6 The graph of y = x is shifted units to the left. This is then vertically stretched by applying a factor of.. Finally, the graph is shifted 8 units upward. 0. The adjacent figure shows a transformation of the graph of y = x. Write the equation for the graph...9. The graph of y = f(x) represents the amount of water.. in thousands of gallons remaining in a swimming pool after x days. a) Estimate the initial and final amounts of water contained in the pool. b) When did the amount of water in the pool remain constant? c) Approximate f() and f(). d) At what rate was water being drained from the pool when x?. Graph the following piecewise-defined function. Is f continuous on its domain?.. Do not use a calculator. x f(x) = + x for x < for x. Given f(x) = 9 x and g(x) = x +, find the following. Do not use a calculator..6. a) (f + g)(x), (f g)(x), (fg)(x); b) the domains of the functions in part a; c) g f and give its domain; d) f o g and give its domain; e) go f and give its domain. Find the difference quotient, Simplify completely. f ( x + h) f( x) h (where h 0 ) for f(x) = x + x An oil well off of the Gulf Coast is leaking, with the leak spreading oil over the water s.6.06 surface as a circle. At any time t, in minutes, after the beginning of the leak, the radius of the circular oil slick on the surface is r ( t) = t feet. Let A ( r) = π r represent the area of a circle of radius r. a) Find ( r)( t) Ao. b) The answer to part a defines the in terms of. c) What is the area of the oil slick after minutes?
5 Answers. a =. a) d = b) M = (6., 7.6). D: (, ) ; R: (, ]. a) ; b) 0; c) ; d) ; Function. a) (, 0); b) (0, ); c) D: (, ) ; d) R: ( ), ; e) m = 6. a) f(x) = x + ; b).6 in. 7. y =.x , 0 ; (0, ) 9a. y = x 8 9b. y =.x a) y = x + 7; b) mph; c) 7 mi.; d) 0.7 mi.. a) y = x 996 b) $0 billion. a) y x 6,7 b) $, contradiction; 6., 7. length: 7 cm; width: 0 cm 8. hr gallons 0. a) C(x) =.0x + 0; b) R(x) = 6.0x; c) 0
6 . P W = L or W = P L. $0,000 at.% and $90,000 at %. a) (, ) ; b) (, ) ; c) (, ) ; d) (, ) ; e) [, ). y = (x + 000). D: (, ) ; R: [, ) 6. Base function: y = x ; shifted left and down 7. y =. x 8. shift right 8; vertically shrink by a factor of ; reflect over the x-axis; shift up 9. y =. x y = x +. a) 0,000 gal; 0,000 gal; b) during the first & fourth days; c) thousand; 0 thousand; d) 000 gal per day. Not continuous.. a) (f + g)(x) = 7x + ; (f g)(x) = x + 7; (fg)(x) = 0x 9x + 8 b) Domain is ( ) f g c) ( x), for all three functions. 9 x = ; D:,, x + d) ( f o g)( x) = 0x + ; D: (, ) e) ( go f )( x) = 0x ; D: (, ). f ( x + h) f( x) h = x + h + A o r t = π t b) area; time c). a) ( )( ) 6π mi 6
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