algebra final.. please see attachment

1 M131 Final Department of Mathematics: MATH 131 Final Exam ANSWERSHEET Name_______________________ Date________________ 1 11 2 12 3 13 14 15 16 17 4 18 19 a)____________ b)_____________ 5 6 20a) MID Point__________ Distance___________ 7 8 20 b) 9 10 a) b) c) Vertical ______________ ___________ _____________ Horizontal/Slant______________ ____________ ___________ 3 5 ) (   x x f x x x f 3 2 ) (   1 2 ) ( 2    x x x x f 2 M131 Final BLANK PAGE LEFT INTENTIONALLY 3 M131 Final Department of Mathematics MATH 131 College Algebra for Math & Science Majors Cumulative Final Exam _____________________________________________________________ _____________ NAME_______________________ INSTRUCTIONS : Write your Final Answers on the ANSWERSHEET . Students are allowed to use Graphing Calculator . Please make sure you write your name on the ANSWERSHEET as well. _____________________________________________________________________________________ 1. What values for x (Domain) that must be excluded in the following fraction? A) B) C) D) 2. Solve the inequality and express the solution in interval notation. )3 2)(3 ( 1    x x x 3 ,3 2  3, 3 2  1,3, 3 2   1,3, 3 2 1 2x 5   4 M131 Final 3) Sketch the graph of f(x) = 4) Graph ; Label the vertex and vertical axis of symmetry . 5) Let f(x) = 3x2 - 7, g(x) = x + 5 ; Find 6) Find the inverse of        0 ; 2 0 ; x x x x 3 2 1) 5(x f(x)       2 fοg 5 3 ) (   x x f 5 M131 Final 7) Find equation of the line passing through the point (1, -1) and perpendicular to 8) U se synthetic division to divide : 9) Divide : ; Note i 2 = -1 10) Find the asymptotes (Horizontal, vertical or slant), if any. Do not Gr aph. a) b) c) 11) Solve : 0 3 2    y x ) x( ) x x x ( 3 12 3 7 4 2      i i   2 1 3 5 ) (   x x f x x x f 3 2 ) (   1 2 ) ( 2    x x x x f 0 2 5 2 2    x x 6 M131 Final 12) Solve: 2x = 128 13) Evaluate using change of base formula. 14) Use the properties of logarithms to expand: 15) Solve: 10 + − = 11 0 16) Solve: 8 + ln(x) = 11 17) Find the balance amount after 5 years if $12,000 is invested at an annual rate of 5% compounded bi-monthly . 18) You have deposited $ 500 in an account that pays 6.75% interest, compounded continuously. How long will it take to double the amount ? ])2 ( [ log 2z y x 7 M131 Final 19) a) Decide whether the graph of is a function or not? Answer in Yes or No, and give reasoning to your response. b) Find the domain of . 20) a) Find the Mid -point and the distance between the points ( -3, 2) and (5, -10) . b) Find the focus and directrix of a parabola whose equation is y2 = 8x. Graph this parabola. __________________ 12 3 5 2 2   y x )2 log( x 8 M131 Final SCRAP WORK SPACE 9 M131 Final SCRAP WORK SPACE