MATH 101 FINAL EXAM Review College Algebra The Final Exam is cumulative Problems will be similar to those you have seen on previous exams The exam is worth 120 points Formulas provided on Exam 4 will also be provided on the Final Part I Multiple Choice The exam will have 15 multiple choice questions which will cover concepts definitions and symbolism The questions will be similar to the MC questions on previous exams Part II The remaining questions will be graded on partial credit Graphs should be clearly labeled Some of the vocabulary and skills to review are included in the following table Vocabulary concepts function zero of a function domain range matrix row echelon form discriminant asymptote rational function systems of equations dependent independent consistent inconsistent 1 f x x2 2x logarithm exponential difference quotient slope transformations composition piecewise function inverse function polynomial function end behavior increasing decreasing constant maximum minimum rate of change basic function families g x 1 x 1 Skills some long division synthetic division interpreting a graph factoring factoring a polynomial quadratic formula u substitution squaring a binomial composing functions interval notation sign test for inequalities h x 3x 5 a Find and simplify f 2 b Find and simplify g h x c Find and simplify i f h x ii f h 1 f x h f x d Simplify the difference quotient h 2 Use the tables for f x and g x to find a f g 3 b g f 3 x f x 1 5 3 7 5 1 7 3 x g x 1 3 3 5 5 7 7 8 3 Write the equation of the line through the points 3 7 and 3 4 Give your answer in slope intercept form 4 Write the equation of the line through 4 5 that is perpendicular to the line 2x 3y 6 0 Give your answer in slope intercept form 5 Describe each transformation Use the graph of y f x given to sketch each transformation a y f x 1 2 b y 12 f x c y f x Math 101 Exam Final Fall 2011 Grading Guide 61 MC Function Substitution V 0 a 2 points 2 points If f x 3x 2 then f x h 6 Graph the piecewise function a 3x 3h 2 2h x 2 2 3b 3xx 0 f x 0 c 3x 2 3h 2x 2 d x 3x 22 h d 2 points 62 MC Function Substitution V 1 2 points If f x x2 then f x h a x2 h2 b x2 h c x3 x2 h d x2 2xh h2 x x 1 or 1 3 points 63 Graphing IntersectingFunctions Inequality V 0 randomization 3 points Use the following figure to find the value s of x for which f x g x 7 Use the graph to solve f x g x 10 f x 8 6 4 2 0 10 8 6 4 2 0 2 2 4 6 8 10 g x 4 6 8 10 8 Graph the function f x x2 2x 6 Label the scale clearly a What is the vertex b State the domain and range c Write the equation for the axis of symmetry d Over what interval s is f x increasing 13 e Over what interval s is f x decreasing f Find the real zero s for f x 9 A cell phone company develops a pay as you go cell phone plan in which the monthly cost varies directly as the number of minutes used If the company charges 17 70 in a month when 236 minutes are used what is the constant of variation What should it charge for a month in which 500 minutes are used 10 Demand for a product varies inversely with the price per unit of the product Demand for the product is 10 000 units when the price is 5 75 per unit What is the constant of variation What is the demand to the nearest hundred units when the price is 6 50 11 The profit that a vendor makes per day by selling x pretzels is given by the function P x 0 002x2 2 8x 200 Find the number of pretzels that must be sold to maximize profit 12 The height of a model rocket launched from a 112 foot cliff is given by h t 16t2 96t 112 where t is the time in seconds from when the rocket is launched Find the maximum height the rocket attains above the cliff 13 Decide whether x 4 is a factor of P x 2x3 14x2 23x 4 14 Describe the end behavior of the graph of f x x4 2x 5 15 For the polynomial function P x x2 3 x 2 x 1 2 list all the zeros and their multiplicities Determine whether the graph of P x touches or crosses at each zero 16 Find all the real or complex zeros of f x 3x3 x2 34x 40 and write P x in factored form 17 Use the Rational Zeros Theorem to list the possible rational zeros for f x 10x3 13x2 103x 20 18 Give the equations for any vertical horizontal or oblique asymptotes of x2 x 2 3x2 4x 5 2x 3 a f x 2 b g x c h x 2 2x x 21 x 2 x 2x 3 19 Sketch a graph of f x 2x 3 Label all intercepts and asymptotes x 1 20 Solve each inequality analytically sign test Verify graphically x 2 x 1 a 0 b x2 5x 4 0 x 4 21 Find a formula for the inverse of f x x 3 a What is the domain for f x b What is the domain for f 1 x 22 a Write in logarithmic form 2 3 0 125 b Evaluate log7 28 c Evaluate ln e3 6 23 Solve for x log2 6x 4 4 1 24 Solve for x 42x 5 1 64 25 Solve for x 2x 3 72x 26 Solve for x e5x 1 4 27 Solve for x 3x2 2x 11 0 28 Solve for x 4x 3 9 29 Use the properties of logarithms to express the following as a sum difference or product of m3 n simpler logarithms log y 30 Suppose 15 000 is invested at 3 25 Find the total amount present at the end of 5 years if interest is compounded a quarterly b continuously 31 If Tim has 1000 to invest at 7 compounded continuously how long will it be before he has 1500 How long before his investment is doubled 32 If Seattle had a population of 2 3 million in 1990 and 1 75 million in 1950 use the continuous growth model A t A0 ekt to find the rate of growth and predict the population for 2015 33 Assume fish populations obey the exponential growth model A t A0 ekt There are 15 angel fish in a fish tank at the beginning of the month Thirty days later there are 55 angel fish a Find an exact representation …