Directions: To receive afull credit Show all steps, label and simplify each answer. You may use a sciemic calculator. You may no! use human help or any solver programs. 1. Given [(1) = L (10:) = 6x 2, and [100 = xZ' 3): 12 4' find the following. 10 pl: 3) The dumain of f(x). Write Ihe answer in inlerval notation. b) The domain of got), Justify your answer. c) (f 0 gm). Simplify the function. d) The damain of (f o g)(x). e) Evaluate and simplify f0!) I100. Page 1 of 7 2. Let f (x) = x2 - 4x. Find the difference quotient for (3 + h) - f(3) h 5 pts 3. Given g(x) = 2 cos ) - 3, 10 pts a) Determine the amplitude. b) Find the period. c) Write the equation of the midline. d) Identify 5 key points for one period. x g (x) e) Sketch a graph of g (x) for two full periods. Page 2 of 74. Find the partial fraction decomposition of x2 + 3x - 18 5 pts 5. Expand the following expression using the properties of the logarithms. Assume x and y are positive. 5 pts In (913) 6. Solve for x. Do you need to check for extraneous solutions for these? 10 pts (a) 3(43x -7) = 48 (b) log, x = - 7. Solve for x. 5 pts log2 (x - 5) + log2(x + 1) = 4 Page 3 of 78. Given sec0 = -6, sketch the angle in standard position and find csco and tan 0, where 0 terminates in quadrant III. 5 pts 9. Find the exact value. 10 pts (a) tan (b)arccos (--z) (c) arctan (tan (-") ) 10. Verify the following trigonometric identity. Justify each step with the identity or property you used. 5 pts sin 0 . cos 0 = tan 0 - tan0 . sin20 Page 4 of 7\f12. Given the polynomial function: 10pm h(x) = 336'9 7x3 - 18x2 + 28x + 24- a) List the possible rational zeroes of Mx). b) Use long division or synthetic division to show that 3 is a zero ofthe given function. c) Find the remaining zeros. d) Write the complete linear factorization of Mx). Page 6 of7 13. Given 4x 33/ = 8, write the equation ofthe line perpendicular to the given line and that passes through the points (-12, 5). 5pm 14. Use the graph of g(x) to answer each question. 5 p1: (a) Find the domain and range of got). Write the answers in interval notation. Domain: Range: (b) Evaluate g( 3). (c) On which interval(s) is the graph increasing, decreasing, or constant? Inc reasin g: Decreasing: Constant: (d) What are the x- and y-intercepts of the graph? Page 7 of