# Fall, 2016, V4.3 This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.

Fall, 2016, V4.3 This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. Record your answers and work on the separate answer sheet provided. There are 28 problems. Problems #1–6 are Multiple Choice. Problems #7–17 are Short Answer. (Work not required to be shown) Problems #18–28 are Short Answer with work required to be shown. 1. Solve, and express the answer in interval notation: | 3 – 8 | ≤ 21. A. (–∞, −9/4] ∪ [3, ∞) B. (–∞, –9/4] C. [–9/4, 3] D. [–9/4, ∞) 1. ______ 2. Which of the following polynomials has a graph which exhibits the end behavior of downward to the left and downward to the right? A. ( ) = –6 – – – 5 B. ( ) = 8 + 6 – + 3 2. _______ C. D. ( ) = 5 + 7 + ( ) = –3 + 9 – – 1 3. Express as an equivalent expression: 8 log + log 1 – log ( – 3) 3. ________ A. log 8 B. + C. log ( ) -13D. -13log 8 + 4 − MATH 115 Precalculus 4. Determine the interval(s) on which the function is increasing. A. (− 4 / 3, 1) B. (−1,1) and (3,∞) Fall, 2016, V4.3 4. ______ C. ( ) 11/ 3, ∞) C. ( ) = − D. ( ) 1 -40 = − + 5. _____ Page of MATH 115 Precalculus 6. Which of the functions corresponds to the graph? A. ( ) = cos(2 ) + 2 B. ( ) = 3 – sin C. ( ) = sin + 3 D. ( ) = 2 cos + 1 : 7. Points (–7, 2) and (5, 6) are endpoints of the diameter of a circle. Fall, 2016, V4.3 6. ______ (a) is the exact length of the diameter? (Simplify as much as possible) Answer: ________ (b) is the center of the circle? (c) is the equation of the circle? Answer: ____________ Answer: ___________________________ 8. Find the value of the logarithm: log Answer: ____________ 9. Bill, a resident of Metropolis, pays Metropolis an annual tax of $55 plus 1.8% of his annual income. If Bill paid $1,441 in tax, what was Bill’s income? Answer: _____________ Page of MATH 115 Precalculus Fall, 2016, V4.3 10. A can of soda at 71° F. is placed in a refrigerator that maintains a constant temperature of 39° F. The temperature of the soda minutes after it is placed in the refrigerator is given by ( ) = 39 + 32 – 0.058 Find the temperature of the soda 20 minutes after it is placed in the refrigerator. (Round to the nearest tenth of a degree.) Answer: ________ 11. Given the function = 3 − , find a formula for the inverse function. Answer: __________________ 12. (a) State the reference angle associated with 300°. (b) Convert 300° to radians. Leave the answer in terms of ð. 13. Given = 9 sin(8 – ð), state the (a) period (b) phase shift Answer: ________ Answer: ________ Answer: ________ Answer: ________ 14. Solve the trigonometric equation (cos )(2cos + 1) = 0 in the interval [0, 360°). Answer: _________________ 15. (a) Find the exact value of arccos sin (b) Find the exact value of arcsin tan 16. For the parabola given by ( + 5) = 8( – 2), find the following: (a) direction parabola opens (to the left, right, up, or down) (b) vertex (c) focus Answer: ________ Answer: ________ Answer: ___________ Answer: ___________ Answer: ___________ Page of 3 + 1 Fall, 2016, V4.3 17. Let ( ) = − 2 (a) State the domain. (b) State the vertical asymptote(s). (c) State the horizontal asymptote. (d) Which of the following represents the graph of ( ) = 3 + 1 − 2 Answer: _________________ Answer: _________________ Answer: _________________ Answer: ______________ GRAPH A. GRAPH C. GRAPH B. GRAPH D. MATH 115 Precalculus . Fall, 2016, V4.3 (a) Find the composite function ( o )( ) and simplify. (b) Find ( o − . 21. A projectile is launched from a platform 15 feet high with an initial velocity of 48 feet per second. The height of the projectile at seconds after launch is given by = –16 + 48 + 15 feet. (a) How many seconds after launch does the projectile attain maximum height? (b) is the maximum height? 22. Solve: − 6 − 4 + 16 −16 = 0 . 23. Suppose that cos è = 5/13 and that è is a Quadrant IV angle. (a) Find the exact value of sin è. (b) Find the exact value of sin(2è ). . 24. the identity (sin + cos ) − sin(2 ) = 1 MATH 115 Precalculus Fall, 2016, V4.3 25. From a point 48 feet from the base of a redwood tree, the angle of elevation to the top of the tree is 52.3°. Find the height of the tree to the nearest tenth of a foot. (sketch is not to scale) 26. For the triangle , we are given that = 46°, = 64°, and = 35.0. Find the length of side , rounded to the nearest tenth. 27. Let = 〈10, –5〉 and = 〈2, 4〉. (b) Calculate the dot product ∙ (c) Determine the angle between and Round the result to the nearest degree. 28. An ellipse has the equation + = 1 (a) Is the major axis horizontal or vertical? (b) Find the exact values of the foci of the ellipse.