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fath)-f(a) 1. If f(x ) = x'- x +6, evaluate the difference quotient h a. 2ath-6 b. 2a- 6 c. 2a- h- 6 d. h e. none of these 2. Find the domain of the function / (x) = -2 sinx - 3 a. (-00, OD) b. c. [-3. - 2] d. [2, 3]3. The graph of the function f is given. State the value of /(-0.4) . a. /(-0.4 ) = 8 b. /(-0.4) = -10 c. /(-0.4) = -8 d. f(-0.4) = 0 e. /(-0.4) = 10 4. Scientists have discovered that a linear relationship exists between the amount of flobberworm mucus secretions and the air temperature. When the temperature is 65-F, the flobberworms each secrete 16 grams of mucus a day; when the temperature is 95 F, they each secrete 22 grams of mucus a day. Find a function M(t) that gives the amount of mucus secreted on a given day, where t is the temperature of that day in degrees Fahrenheit. a. M(t ) = 0.2 + 16 b. M(t) = 5 +16 c. M(() = 5: +3 d. M(t) = 0.2+35. Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations. y = 4+2x - x' a. C. -2+ - 3 . b. d. 1 2 +\f7. The graph of the function /(x) = x - 11x +7 has been stretched horizontally by a factor of 2. Find the function for the transformed graph. g(x) = x* - 11x +7 2 b. g(x) = 2x3-22x + 14 C. x* - 22x + 28 {(x) = d. g(x) = 4x' - 22x +7 8. A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after / minutes. When the data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute. The monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the patient's heart rate after 42 minutes using the secant line between the points with f = 38 and / = 42. (mins) 36 38 40 42 44 Heartbeats 2570 2720 2840 3020 3070 . 74 b. 80 C. 85 d. 70 e. 76 f. 75 9. If a ball is thrown into the air with a velocity of 58 ft/s, its height (in feet) after / seconds is given by H = 581 - 9ra. Find the velocity when f = 9. a. -101 fu/'s b. -104 fu/'s C. -106 fu/s d. -103 ft/s e. -99 fu/'s10. The position of a car is given by the values in the following table. z (seconds) 0 2 3 4 s (meters) 0 21.9 25.8 69.2 92.2 Find the average velocity for the time period beginning when z = 2 and lasting 2 seconds. a. 46.1 fu/s b. 31.9 fu/s c. 33.5 ft/s d. 33.8 fu/s e. 33.2 ft/s 11. Suppose the distance s (in feet) covered by a car moving along a straight road after t sec is given by the function s= f(t) = 3 + 13t. Calculate the (instantaneous) velocity of the car when t = 35. a. 223 ft/sec b. 16 ft/sec c. 560 ft/sec d. 4130 ft/sec12. Sketch the graph of the function f and evaluate lim f(x). *+-3+ f(x) = x+5, ifx s-3 [-2x - 1, ifx > -3 a. C. + + Does not exist Does not exist b. d. 5\f16. Use the graph of f(x) = * +x- 2 x'+x-2 to guess at the limit lim -, if it exists. x+2 *+ -2 x +2 4+ a. -2 b. -1 c. Does not exist d. -3 17. Let F(x)= x - 5 1x - 51 Find the following limits. lim F(x), lim F(x ) x-45+ a. both 1 b. 2 and 1 c. 2 and-1 d. 1 and-1 e. both-118. Which of the given functions is discontinuous? a. x # 11 f(@) = x- 11 9. x = 11 b. x 211 f(x) = x - 2 x 1 H. -2 b. 2 C. 1 d. 0 20. Find the interval(s) where f(x) =
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