MATH 115 Precalculus Fall, 2017, V1.1 MULTIPLE CHOICE 1. Solve, and express the answer in interval notation: 7 4 x 5. A. B. C. D. 1. ______ (-, 1/2] [3, ) (-, 1/2] [1/2, 3] [1/2, ) 2. Which of the following polynomials has a graph which exhibits the end behavior of upward to the left and downward to the right? 2. _______ vvvv f (x) = 4x3 + x + 8 f (x) = -5x6 - 9x2 - 5 f (x) = 7x4 - 3x2 - x f (x) = -8x5 + 7x3 - x - 5 A. B. C. D. 3. Write as an equivalent expression: log x + log 1 - 3 log y 3. ______ A. log(x+1- 3y) B. log( x +1 3y log x+1 y C. 3 ( ) D. log ( yx ) 3 4. Determine the interval(s) on which the function is decreasing. 4. ______ Page 1 of 9 MATH 115 Precalculus A. (-, - 4) and (1, ) B. (- 4, 1) C. (- 5.5, -2) D. (-, -2) Fall, 2017, V1.1 5. Which of the functions corresponds to the graph? 5. ______ A. f (x)=ex B. f (x)= ex 1 C. f (x)=ex +1 D. f (x)= ex +1 6. Which of the functions corresponds to the graph? 6. ______ Page 2 of 9 MATH 115 Precalculus Fall, 2017, V1.1 A. f (x) = cos(2x) + 2 B. f (x) = sin x + 3 C. f (x) = 2 cos x + 1 D. f (x) = 3 - sin x SHORT ANSWER: 7. Points (1, -3) and (7, 1) are endpoints of the diameter of a circle. (a) What is the exact length of the diameter? (Simplify as much as possible) Answer: ________ (b) What is the center of the circle? Answer: ____________ (c) What is the equation of the circle? Answer: ___________________________ Page 3 of 9 MATH 115 Precalculus 9. Fall, 2017, V1.1 Paul, a resident of Metropolis, pays Metropolis an annual tax of $50 plus 1.7% of his annual income. If Paul paid $1,019 in tax, what was Paul's income? Answer: _____________ 10. A can of soda at 82 F. is placed in a refrigerator that maintains a constant temperature of 35 F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by - 0.058 t T(t) = 35 + 47 e 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 5 1 f(x)= 6 4 x , find a formula for the inverse function. Answer: __________________ 12. (a) State the reference angle associated with 225. (b) Convert 240 to radians. Leave the answer in terms of . Answer: ________ Answer: ________ 13. Given y = 5 sin(6x - ), state the (a) period Answer: ________ (b) phase shift Answer: ________ 14. Solve the trigonometric equation (cos x)(2 sin x + 1) = 0 in the interval [0, 360). Answer: _________________ Page 4 of 9 MATH 115 Precalculus 15. Fall, 2017, V1.1 3 A: find the exact value of arccos (tan 4 ) Answer: _________________ 5 B: find the exact value of arcsin (sin 6 ) Answer: _________________ 16. For the parabola given by (x - 1)2 = -8(y - 3), find the following: (a) direction parabola opens (to the left, right, up, or down) Answer: ___________ (b) vertex Answer: ___________ (c) focus Answer: ___________ 17. Let f (x)= (a) State the domain. 2x 3+ x Answer: _________________ (b) State the vertical asymptote(s). Answer: _________________ (c) State the horizontal asymptote. Answer: _________________ (d) Which of the following represents the graph of GRAPH A. f ( x )= 2x 3+ x Answer: ______________ GRAPH B. Page 5 of 9 MATH 115 Precalculus GRAPH C. Fall, 2017, V1.1 GRAPH D. SHORT ANSWER, with work required to be shown, as indicated. 18. Find the equation for a line which passes through the points (4, -1) and (8, -9). Write the equation in slope-intercept form. Show work. 19. Find the exact solutions and simplify as much as possible: 3x2 + 6 = 10x. Show work. Page 6 of 9 MATH 115 Precalculus Fall, 2017, V1.1 20. Let f (x) = 4x2 + 8 and g(x) = x 1. (a) Find the composite function( f og)(x)and simplify. Show work. (b) Find ( f og)(3). Show work. 21. A projectile is launched from a platform 10 feet high with an initial velocity of 48 feet per second, The height h of the projectile at t seconds after launch is given by h = -16t2 + 48t + 10 feet. (a) How many seconds after launch does the projectile attain maximum height? (b) What is the maximum height? 22. Solve: x +10 32 + 2 =0 x +2 x 4 Show work. Show work. Show work. 23. Suppose that sin = 5/13 and that is a Quadrant II angle. (a) Find the exact value of cos . Show work. (b) Find the exact value of sin(2 ). Show work. 24. Prove the identity (cos x + sin x)2 - 1 = sin(2x) 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. Show work. (sketch is not to scale) Page 7 of 9 MATH 115 Precalculus Fall, 2017, V1.1 26. For the triangle ABC, we are given that A = 40, B = 63, and c = 38.0. b Find the length of side , rounded to the nearest hundredth. Show work. 27. Let u = 9, 3 and v = 2, 6. u (b) Calculate the dot product (c) Determine the angle between work. u v . Show work. and v . Round the result to the nearest degree. Show Page 8 of 9 MATH 115 Precalculus 28. An ellipse has the equation Fall, 2017, V1.1 4 x 2 9 y 2 (a) Is the major axis horizontal or vertical? (b) Find the exact values of the foci of the ellipse. Show work. Page 9 of 9