Math 101 Chapter Four Practice Eam Questions SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. What is the domain of f()? What is its range? 1) f() = 1-1 + 3 1) 2) f() = -1 ( - 2) 2 + 1 2) What are the equations of the vertical and horizontal asmptotes of the graph of the given equation? 3) = 1 ( - 1) 2 + 3 3) Is f() an even or odd function? What smmetr does its graph ehibit? ) f() = - 1 2 ) Eplain how the graph of f can be obtained from the graph of = 1 or = 1 2. 5) f() = - 0.7-7 5) 6) f() = 1 ( - ) 2 + 9 6) 7) f() = -7 ( + ) 2 7) ) f() = -7 ( + 12) 2 ) 1
Sketch the graph of the function. 9) f() = 1-3 9) 2 - -2 2 6-2 - 10) f() = 2 10) 10-10 10-10 Rewrite f() = (a + b)/( + c) in f() = a + d/( + c) form. 11) f() = -2-3 + 2 11) 12) f() = 3-5 - 2 12) 2
Graph f() b rewriting f() = (a + b)/( + c) in f() = a + d/( + c) form. 13) f() = -2-3 + 2 13) - - - - 1) f() = 3-5 - 2 1) - - - - Give the equations of an asmptotes of the tpe specified for the graph of the rational function. 15) f() = - 9 2 ; vertical 15) + 16) f() = + ; oblique 16) 5 2 + - 17) f() = 2 + - 1 ; horizontal 17) - 1 3
Sketch the graph the rational function, including all asmptotes. 1) f() = 2 - - 2 1) 19) f() = 2 2 - - 20 19) 20) f() = - 2 2-20)
Sketch the graph of the rational function, including all asmptotes. Provide other information as requested. 21) f() = ( 2-1)(5 + ) (2-25)(1 + ) 21) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Choose the equation that matches the rational function graphed. 22) 22) 6 2 - - -2 - A) f() = - 5 + 5 C) f() = ( + 5) 2 ( - 5)( + 5) B) f() = D) f() = ( - 5) 2 ( + 5)( - 5) ( + 5) 2 ( - 5)( + 5) 5
23) 23) 6 2 - -6 - -2-2 2 6 - -6 - A) f() = 2 2 + - 12 C) f() = 2 2 - - 12 B) f() = - 2 2 + - 12 D) f() = - 2 2 - - 12 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the rational function and all asmptotes. Label the coordinates of an points where the graph of f intersects its oblique asmptote. 2) f() = + 3 + 2-2 + 1 3 + 1 2) 2 - -2 2-2 - Solve the rational equation. 25) ( - 9) 2 = 0 25) 26) 1 + 6 = 5 26) 6
Solve the rational inequalit. 27) 9 + > 6 5 27) 2) 1-2 + 1 + 2-2 3 2) 29) 7 + 3 7 2 + 2 > 0 29) 30) -6 2 + 1 < 0 30) Find all comple solutions for the equation. 31) 6-2 - + 2 = 2-31) 32) 1-17 + 6 2 = 0 32) 33) 2-2 + -1 + 2 = 0 33) Solve the problem. 3) At a single ticket booth, customers arrive randoml at a rate of per hour. The average line length is given b f() = 2 00-20, where 0 < 20. To keep the wait in line reasonable, it is required that the average line length should not eceed 10 customers. Determine the range of rates at which customers can arrive before a second attendant is needed. Epress our answer in interval form. 3) 35) If f varies jointl as q 2 and h, and f = 36 when q = 3 and h = 2, find q when f = 192 and h = 6. 35) 36) Suppose varies directl as the square of and inversel as m. If = 9 when = 2 and m =, find when = and m = 6. Round to the nearest hundredth when necessar. 36) 37) Hooke's Law for an elastic spring states that the distance a spring stretches varies directl as the force applied. If a force of 25 pounds stretches a certain spring 6 inches, then how much will a force of 100 pounds stretch the spring? 37) Evaluate the epression without using a calculator. 3) 100 3/2 3) 7
39) ( 3-1000) 2 39) Use positive rational eponents to rewrite the epression. Assume variables are positive. 0) 3 z 2-2 0) 1) + 1 7 + 1 1) Determine the domain of the function. 2) f() = 7-10 2) 3) f() = 3 9-2 3) Graph the function b hand. Solve the equation f() = 0 b observing our graph. Round approimations to two decimal places. ) f() = - ) 5) f() = 5 2 + 5)
Use transformations to eplain how the graph of the given function can be obtained from the graph of the appropriate root function ( = or = 3 ). 6) f() = 36 + 1 6) 7) f() = 3 125 + 250 7) Describe the graph of the equation as either a circle or a parabola with a horizontal ais of smmetr. ) ( - 1) 2 + ( + 5) 2 = 25 ) 9) = 2 + + 9) Use the calculator graph to find the solution set of the given equation or inequalit. 50) - 2-50) -2 Intersection X = 6 Y = 2 Begin b drawing a rough sketch to determine the number of real solutions for the equation 1 = 2. Then use an analtic method to confirm our answer. Give the solution set and an etraneous values that ma occur. 51) 1 = 51) 2 = - + 9
52) 1 = 2 = + 52) Use an analtic method to solve the equation. 53) - 3 = 2-3 53) 5) 2 + 3 - + 1 = 1 5) 55) + 6 + 2 - = 55) 56) + 1 = 2 56) 57) (2 + 3) 1/2-1 = ( + 1) 1/2 57) 5) ( + 10) 2/5 = (9) 1/5 5) 59) 5-2 - 2-1 - 3 = 0 59) Solve the equation involving "nested" radicals for all real solutions analticall. 60) 3 2 + 5 = 3 2 + 3 60) 10
Solve the problem. 61) Fred is in a row boat that is 5 miles from the shore of a lake. He wants to get to his house, which is miles down the shore, as shown below. He will row to shore and then jog the remaining distance along the shore. He can row at 3 miles per hour and can jog at 6 miles per hour. At about what point along the shore should he beach the boat and jog the rest of the wa if he wants to get home as soon as possible? Round our answer to the nearest tenth of a mile, if necessar. 61) 5 miles miles 62) The battleship USS Tennessee is 110 miles due south of the destroer USS Alaska and is sailing north at 0 mph. If the USS Alaska is sailing east at 25 mph, how far apart will the ships be when that distance is at a minimum? Round our answer to the nearest tenth of a mile. 62) 11