AP Calculus Summer Assignment Name: Note: Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers for which f () is a real number. Part : Multiple Choice Solve each of the following problems, using available space for scratchwork. After eamining the form of the choices, decide which is the best of the choices given. Do not spend too much time on any one problem.. The domain of f ( ) is all all, (C) all (E) all reals. The graph of 3 y is symmetric with respect to which of the following? I. The -ais II. The y-ais III. The origin I only II only (C) III only II and III only (E) I, II, and III
5 3. The epression is equivalent to (C) 5 (E) 3 4. If f ( ) 3 and if c is the only real number such that f ( c) 0, then c is between - and - - and 0 (C) 0 and and (E) and 3 b b 5. If log b (3 ), then b = 9 3 (C) 3 (E) 9 Page of 9
6. If f is a function such that f ( 0), f ( ), and what is the value of f (4)? f ( n ) f ( n) for all integers n 0, f ( n ) 8 3 (C) (E) It cannot be determined from the information given. 3 7. The function f ( ) 5 has eactly one real zero. It is between - and - - and 0 (C) 0 and and (E) and 3 ln( 3 e ) 8. 3(ln e ) 3ln (C) ln( 3 e ) 3ln (E) ln Page 3 of 9
9. Which of the following functions is not odd? f ( ) sin f ( ) sin (C) f ( ) 3 f ( ) (E) f ( ) 3 a 0. The epression b is equivalent to a b a b a b a b a b (C) a b a b (E) -. Which of the following is the equation of the line that passes through the point (a, b) and is parallel to the -ais? (C) (E) a b y a y b b a Page 4 of 9
. If the graph of a function f is symmetric about the y-ais and contains the point (-, ), which point is also on f? (-, -) (, -) (C) (0, 0) (, ) (E) (, ) 3. If f ( ) and g ( ), then f ( g( )) g( f ( )) when = (C) - (E) 0 Part : Free-Response SHOW ALL YOUR WORK WHERE POSSIBLE. Indicate clearly the methods you use because you will be graded on the correctness of your methods as well as on the accuracy of your final answers. If you choose to use decimal approimations, your answers should be correct to three decimal places. 4. Complete the chart with eact values only. These values must be memorized for AP Calculus. sin 0 3 6 3 4 cos tan Page 5 of 9
5. Consider g ( ) 4 This is called a piecewise function. If you have never seen something like this before, consider it a challenge. Perhaps you might need to do a little research on the internet. Your knowledge of domain and range and graphing functions is of utmost importance. a. Find g(-3), g(0), g() and g(3) b. Sketch the graph of g(). 6. Sketch the graph of asymptotes. 4 8 f ( ). Identify any intercepts and vertical and/or horizontal Page 6 of 9
7. a. Sketch the graph of the function y 3. b. Identify the intercepts and any maimum or minimum points. 8. Factor each polynomial: a. 6 5a b. - 7 + 3 c. 3 d. + 5 6 Page 7 of 9
9. The standard equation for converting Celsius (C) temperature to Fahrenheit (F) temperature is a linear equation. If we plot Fahrenheit temperature against Celsius temperature in the coordinate plane, the points lie in a line. The line passes through the point (0, 3) because F = 3 when C = 0. It also passes through the point (00, ) because F = when C = 00. Use this information to write an equation for the line. 0. a. If f () = + and g () =, find (f g) (3). b. If f() = 3 and g() = 3, then find f (g (3)). Write the equation of a circle whose center is at (3, 4) and has a radius of 5. Sketch the circle. Page 8 of 9
. Name the type of graph for each equation. Sketch the graph. If a graph has an intercept or a verte, be sure that it is clearly marked in your sketch. a. ( ) + y = 4 b. + y = 4 c. 4 + y = 4 d. y 4 e. y 4 f. y = e g. y = ln Page 9 of 9