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# Math 96 Final Review Sheet

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Math 96 Final Review SheetGraphing: Find a complete graph of the functions below, plotting at least 3 pointsand finding any major characteristic points (vertex, asymptotes, etc.)Find the Domain and Range of #1-15 too.1) 8 1 also find the vertex, x & y-intercepts, axis of symmetry, max/minC œ #B  B #2) 0ÐBÑ œ #B"3) log 1ÐBÑ œ B#4) 0ÐBÑ œ B  &È5) 0ÐBÑ œ lB  "l  #6) also find vertex, x & y-intercepts, axis of symmetry, max/min0ÐBÑ œ  \$B  'B  "#(Ñ 1ÐBÑ œ  ÐB  \$Ñ  ## also find vertex, x & y-intercepts, axis of symmetry, max/min)Ñ C œ Ð Ñ"\$B*Ñ 0ÐBÑ œ /  "B"!Ñ C œ  Bln""Ñ C œ  B  "  "È"#Ñ 0ÐBÑ œ B  %log&"\$Ñ 0 B œ B  \$  ""#  # also find vertex, x & y-intercepts, axis of symmetry, max/min"%Ñ 'B  *C  ") œ !"&Ñ 0 B œ  ""# Œ B"'Ñ \$B  #C Ÿ )Graph the solution set to the system of inequalities:"(Ñ #B  C Ÿ " B  C  " and 18) B Ÿ ! C  ! C  B  # C Ÿ B  "Evaluate the following logs without using a calculator:19) a) log b) log c) log d) log% & '" "& "!!"' ' Ð ÑÈ log f) ln e g) ln e h) ln /Ñ "'#"/ i) ln 1 j) log(È"!ÑSolve the following multiple choice questions:20) If is the function 0 0 œ Ö Ð#ß \$Ñß Ð"ß #Ñß Ð!ß &Ñß Ð"ß #Ñß Ð&ß !Ñ ×Þ Then the range of is:0 a) { b) c) d) #ß "ß !ß "ß &× Ò#ß &Ó Ò !ß & Ó Ö !ß #ß \$ß & ×21) The domain of the function represented by the accompanying graph is a) [ , ] b) [ c d! * #ß % Ó Ñ Ö#ß "ß !ß "ß #ß \$ß % × Ñ Ö!ß "ß #ß \$ß %ß &ß 'ß (ß )ß *×22) Which of the following is a function. I. II. III. IV. B C B C Ö Ð"ß #Ñß Ð#ß "Ñ ×# % " ## & # #\$ ' \$ # a) I only b) I and III only c) II only d) II and III only e) I, III, and IV23) Let be the function .0 Ö Ð #ß \$ Ñß Ð  "ß % Ñß Ð !ß ' Ñß Ð "ß # Ñß Ð &ß ! Ñ × The argument having an image is# a) b) ( , ) c) ( , ) d) \$ # \$ " # "24) Express in interval notation: AND B   # B  \$ a) ( , ) b) c) d) e)  # ∞ Ð  #ß \$Ñ Ð  ∞ß  #Ñ ∪ Ð\$ß ∞Ñ Ð  ∞ß ∞ Ñ g25) Express in interval notation: OR B Ÿ # B  ' a) b) c) d) e) Ò #ß ' Ñ Ð  ∞ß #Ó Ð  ∞ß 'Ñ Ð  ∞ß # Ó ∪ Ð'ß ∞ Ñ gSolve the following equations or inequalities:26) "" Ÿ  ")\$B"##(Ñ \$  %B  " \$  %B  * OR#)Ñ B  % œ  \$#  ##*Ñ #B  )B  \$ œ ! # Use the quadratic formulaÞ\$!Ñ C  #!C œ ' Þ # Use the quadratic formula\$"Ñ 'B  #( œ ! #Simplify the following expressions:32) \$  (3#  &333) Œ ")#\$34) 3%\$35) ÈÈ% \$'36) È"'C%\$(Ñ Ð#  \$3Ñ #\$)Ñ ÈÈ\$%BBLet Find the following:0 ÐBÑ œ #B  B  &Þ#39) 0Ð  #Ñ%!Ñ 0Ð+  2Ñ%"Ñ 0 Ð+  2Ñ  0 Ð+ÑSolve the following systems using any method:42) #B  &C œ "#B  %C œ '43) B  C  D œ "#B  D œ %B  #C  %D œ \$Use matrices and row operations to solve this linear system. 44) 2B  C  \$D œ "\$B  C  D œ  #\$B  #C  #D œ "\$Solve the following application problems:45) The cost in dollars of manufacturing compact discs is given byG BG B œ B  '!!B  #!!ß !!!Þ "## a) Find the number of compact discs that must be manufactured to minimize the cost. b) Find the minimum cost.46) Eight flats of impatiens and two flats of marigolds cost \$ . Three flats of"&Þ&!impatiens and five flats of marigolds cost \$ Find the price per flat of each"!Þ!#Þkind of flower.47) The Pool Fun Company has learned that by pricing a newly released Fun Noodleat \$3, sales will reach 10,000 Fun Noodles per day during the summer. Raisingthe price to \$5 will cause the sales to fall to 8,000 Fun Noodles per day.Assuming that the relationship between sales price and number of Fun Noodles islinear,a. Write two ordered pairs given in this problem situation. Let representBprice and let represent sales.Cb. Find the slope for the linear function.c. Interpret the slope.d. Write an equation in function form describing the relationship betweenprice and sales.e. Find the -intercept of your linear function.Cf. Interpret the meaning of the -intercept in this problem situation.Cg. Find the -intercept of your linear function.Bh. Interpret the meaning of the -intercept in this problem situation.B i. Graph the function for the problem situation on the previous page. j. Write the implied domain and range of this function.48) The model gives the minimum wage, in year where E œ "Þ'/ Eß >ß > œ !Þ!\$*>represents the year 1970. Use the model to find the minimum wage in the year1990.49) Inver Hills Community College has decided to supply the learning center withcolor monitors. A meeting with the supplier has led to the following information.4 CGA monitors and 6 VGA monitors can be purchased for \$4600, while 6 CGAmonitors and 4 VGA monitors will cost \$4400. What are the prices of a singleCGA monitor and a single VGA monitor?50) The linear function models the percentage of U.S. men, ,C œ  !Þ%B  \$) Csmoking cigarettes years after 1980.B a) Find and interpret the meaning of the slope. b) Find and interpret the meaning of the y-intercept. c) Predict the percentage of U.S. men who will be smoking in 2010.51) A building measures a height of 500 feet. A ball is thrown upward from the top ofthe building with an initial velocity of 10 feet per second. The height of the ball 2in feet after seconds is given by the equation:> 2Ð>Ñ œ  "'>  "!>  &!!# a) Find the maximum height of the ball. b) Find when the ball will hit the ground.Solve the following Sequences and Series problems:52) Expand and evaluate: 3œ!\$3Ð  "Ñ 3x53 Ñ  #ß \$ß )ß "\$ß Þ Þ Þ a) ________________+ œ\$! b) ________________W œ\$!54) 1 4ß  ß "'ß  '%ß Þ Þ Þ a) ________________+ œ"# b) _______________ W œ"#Answers:1) 2) 3) 4) V(2,-9) D: D: 0 D: [5Ð  ∞ß ∞Ñ Ð ß ∞Ñ ß ∞Ñ x-int: 4.121,

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