MATH 115 Precalculus Fall, 2015, V3.2

Page 3 of 7 6. Which of the functions corresponds to the graph? 6. ______ A. f (x) = 2 + cos x B. f (x) = 2(1 – cos x) C. f (x) = 3 – cos x D. f (x) = 2 – sin x SHORT ANSWER: 7. Points (8, –1) and (6, –5) 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: ___________________________ 8. Find the value of the logarithm:log . Answer: ____________ 9. Amanda, a resident of Metropolis, pays Metropolis an annual tax of $50 plus 2.7% of her annual income. If Amanda paid $1,535 in tax, what was Amanda’s income? Answer: _____________ MATH 115 Precalculus Fall, 2015, V3.2 Page 4 of 7 10. A bowl of soup at 185° F. is placed in a room of constant temperature of 75° F. The temperature T of the soup t minutes after it is placed in the room is given by T(t) = 75 + 110 e – 0.075 t Find the temperature of the soup 24 minutes after it is placed in the room. (Round to the nearest degree.) Answer: ________ 11. Given the function =19 -13 , find a formula for the inverse function. Answer: __________________ 12. (a) State the reference angle associated with 300°. Answer: ________ (b) Convert 300° to radians. Leave the answer in terms of p. Answer: ________ 13. Given y = 3 sin(8x – p), state the (a) period Answer: ________ (b) phase shift Answer: ________ 14. Solve the trigonometric equation (cos x)(2sin x - 1) = 0 in the interval [0, 360°). Answer: _________________ 15. (a) Find the exact value of arcsin sin Answer: ________ (b) Find the exact value of arccos sin Answer: ________ 16. For the parabola given by (x – 4)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: ___________ MATH 115 Precalculus Fall, 2015, V3.2 Page 5 of 7 17. Let 3 1 ( ) 2 x f x x + = - . (a) State the domain. Answer: _________________ (b) State the horizontal asymptote. Answer: _________________ (c) State the vertical asymptote(s). Answer: _________________ (d) Which of the following represents the graph of 3 1 ( ) 2 x f x x + = - ? Answer: ______________ GRAPH A. GRAPH B. GRAPH C. GRAPH D. MATH 115 Precalculus Fall, 2015, V3.2 Page 6 of 7 SHORT ANSWER, with work required to be shown, as indicated. 18. Find the equation for a line which passes through the points (–1, 1) and (–3, 7). Write the equation in slope-intercept form. Show work. 19. Find the exact solutions and simplify as much as possible: 7x2 - 2 = 2x. Show work. 20. Let f (x) = 5x2 + 7 and g(x) = x – 2. (a) Find the composite function ( f o g)(x) and simplify. Show work. (b) Find ( f o g)(-1) . Show work. 21. A projectile is launched from a platform 8 feet high with an initial velocity of 112 feet per second, The height h of the projectile at t seconds after launch is given by h = –16t2 + 112t + 8 feet. (a) How many seconds after launch does the projectile attain maximum height? Show work. (b) What is the maximum height? Show work. 22. Solve: 2 11 56 0 4 16 x x x + + = + - . Show work. 23. Suppose that cos q = 5/13 and that q is a Quadrant IV angle. (a) Find the exact value of sin q. Show work. (b) Find the exact value of sin 2q. Show work. 24. Prove the identity (sin x + cos x)2 – 1= sin 2x MATH 115 Precalculus Fall, 2015, V3.2 Page 7 of 7 25. From a point 63 feet from the base of a redwood tree, the angle of elevation to the top of the tree is 51.8°. Find the height of the tree to the nearest foot. Show work. (sketch is not to scale) 26. For the triangle ABC, we are given that A = 46°, B = 64°, and c = 35.0. Find the length of side b rounded to the nearest hundredth. Show work. 27. Let = 4, 6 and = 12, –8. (b) Calculate the dot product · . Show work. (c) Determine the angle between and . Round the result to the nearest degree. Show work. 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. Show work.