Math 110 Final Exam Fall 2017 Key EXAM A x k x k x n x n f x c x n d x k x n 1 Identify the vertical asymptote s for the function a x k x n b x k 2 Solve the given equation for the variable x Give exact answer ln M 6x 3 a e3 M 6 b e3 M 6 c 3e M 6 d 3e M 6 3 Identify the function that has a horizontal asymptote at y 0 a f x 6 x a 4 x p b f x 4 x a 6 x p c f x 6 x a 6 x p d not enough information 4 Mark buys one coffee and four donuts for a total of 12 Linda buys two coffees and three donuts for a total of 12 Choose the best strategy to determine the cost of a donut c Solve the system x 4y 12 2x 3y 12 b Solve the system x 2y 12 4x 3y 12 a Solve the equation x 4y 2x 3y 5 An investment of 3600 earns an annual interest rate of 4 compounded continuously How long will it take for the investment to grow to a value of 7200 a t 6 Suppose log m expression 2 find the exact value of the given 4 log n 100 and log w d t log 2 0 04 ln 2 4 ln 2 0 04 log 2 t t b c 4 d Solve the equation 3x 7y 24 log m n w3 b 48 a 60 c 5 d 5 1 Math 110 Final Exam Fall 2017 Key EXAM A 7 Basic transformations are applied to the graph of the original function y f x as shown below Original graph of y f x Transformation graph of y f x Identify the formula of the transformation graph of y f x c y f x 1 b y f x 1 a y f x 1 2 2 8 Choose the statement that best describes the function with the given graph 2 d y f x 1 2 a Polynomial function b Quadratic function c Exponential function d Rational function 9 The graph of the quadratic function f x ax2 bx c is shown below b positive c zero d not enough information The value of b2 4ac is a negative 2 Math 110 Final Exam Fall 2017 Key EXAM A 10 The graph of a polynomial function of degree 3 is shown below Determine the function formula for the graph b 2 x 1 2 x 1 2 x 1 2 x 1 f x x 3 f x x 3 f x x 3 a c 11 Find the radius of the circle with equation x2 y2 14x 18y 6 0 x2 14x 49 y2 18y 91 124 radius 124 Give exact answer f x x 3 d 12 Find the slope of the line with equation 3 x y 3x 3y 7x 5 3y 4x 5 5 y 3 4 3 slope x 4 3 7x 5 13 A ball is launched vertically upward from the top of a platform 5 feet tall with an 3 Math 110 Final Exam Fall 2017 Key EXAM A initial velocity of 96 feet per second The height h in feet of the ball above the ground after t seconds is h 5 96t 16t2 What is the maximum height reached by the ball max height occurs when t 3 96 2 16 5 288 144 149 max height 5 96 3 16 3 2 14 Write the equation of the line that is parallel to the line 24x 4y 8 0 and passes through the point 7 2 4y 24x 8 y 6x 2 slope 6 desired line y 2 6 x 7 y 6x 44 15 Construct an equation for the circle shown below where point C is the center of the circle 4 Math 110 Final Exam Fall 2017 Key EXAM A C h k Q 1 4 P 3 8 center point 1 3 2 4 8 2 6 2 radius 3 2 r 2 equation x 2 2 y 6 8 6 2 5 2 5 16 Find the solution for the given system of equations Give exact answer 4 24x 20y 32 6x 5y 8 6 24x 18y 108 4x 3y 18 38y 76 y 2 4x 3 2 You must show work that supports your answer 18 4x 12 solution x 3 y 2 x 3 17 Simplify the given expression Write answer in factored form reduced to lowest terms using only positive exponents 5 Math 110 Final Exam Fall 2017 Key EXAM A 3 2 9x 6y5 y 7x4 9y12 x10 3 2 3 2 9y7 y5 x4x6 27 y18 x15 18 Find all solutions to the equation Give exact answer x x 1 x2 x 2 6x x x 2 x2 2x x 1 6x 0 x2 7x 1 0 7 49 4 1 x 2 x 1 7 45 6x x 2 2 19 Determine the interval s where the graph of the given function is above the x axis Give answer using interval notation 6 Math 110 Final Exam Fall 2017 Key EXAM A 9 x x 5 x 11 f x 11 9 x x2 5x 66 5 9 solution 11 5 9 20 Solve the inequality Give answer using interval notation 2x 3 5 5 2x 3 5 2 2x 8 1 x 4 solution 1 4 7
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