Name: #: Graphing Lines, Parabolas, and other Functions I. No Calculator: Sketch a graph of each equation... - - - - - -.. 6. - - - - - - 7. 8. 9. - - - - - -
... a f - - - - - - II. Use a graphing calculator and its programs for the following problems.. Graph 8 -intercept = -intecepts = verte = (, ). Graph on our calculator. -intercept = -intecepts = The coordinates for: a. the local high point: b. the local low point:
. Graph on our calculator. -intercept = -intecepts = Relative a. ma value: b. min value: #9: Properties of Functions I. Domain and Range: Indicate the domain and range of each equation in interval notation. Do not use a calculator on this first section.. Domain: Range:. Domain: Range: II. Find the domain and range of each equation. You ma use a calculator.. ln Domain: Range:. Domain: Range: III. Answer the following questions.. Consider the function: a. Can be negative? b. Can =? c. What is the domain? 6. Consider the function: a. Can be negative? b. Can =? c. Can be greater than? d. What is the domain?
IV. Given the functions f 7. f b g 7 and gbg find b g 8. gbg 9. fbg b g. fcgbgh. gc fbgh. g 7.. f. g. f h) V. Epand the given binomial. 6. b g VI. Answer the following questions regarding 7. The graph of has been shifted. Write the new equations below. a. b. 7. Paste Pics here 8. The graph of has been shifted. Write the new equations below. 8. a. b. 9. 9. Match the equations listed to the graphs a. b b b b g g g g b. c. d.
#8: Trigonometric Functions I. For each degree measurement give the radian equivalent. =. =. = II. For each radian measurement give the degree equivalent. 6 =. = 6. = 6 III. Use trigonometr to solve for the missing pieces of each triangle. 7. 8. 6 6 V. Graph the following sinusoids. F 9. H G I cos K J 7. sin b 6 g VI. Write trig functions for the following graphs and descriptions.. For this graph write an equation in terms of sine or cosine... =. Fill in the Trig. Table at the back of this packet with eact values for all 6 trig. functions.
#7: Trigonometric Identities and Equations I. Simplif the following epressions using identities and eact values.. sincos. sincos cossin b g b g. coscos sin sin. sin cos III. Simplif the following epressions. F HG. cos I K J A 6. tanb Ag IV. Consider the function cos and answer the following 7. Can take on an real value? 8. How large can cos become? 9. How small can cos become?. How large can cos become?. How small can cos become?. What is the domain and range of this function? Domain: Range: V. Solve the following equations if. Solve & without a calculator and then on -8 use our calculator.. cos. sin cos ***Hint: For -8, graph the left and right sides of the equation separatel and find the intersection points.. cos. 7 6. sin. 7. sin. 8. sin ln 6
#6: Absolute Value and Piece-wise Functions I. Graph the following absolute value function, and then write a piece wise function to represent it.. - - II. Graph the following piece-wise function.,. f R b g S T, 6, - - IV. Use our calculator to graph and then eplain what ou observe.. - - - -. Observation: 7
#: Solving Equations (Algebraicall & on a Calculator) I. Solve the following algebraicall:. Use Factoring. Quadratic Formula 6 6 8 II. Solve the following using our graphing calculator. Make sure to write all answers rounded to decimal places. Include a sketch of our graph.. 8. 8 V. Solve the following algebraicall.. 7 6. 8
#: Eponential Functions, Inverses, Circles and OIT s (Other Interesting Things) I. Solve the following for. Do not use a calculator on problems -.. 6. 8. e. 8.. 76 6. e.6 7 II. Use our log rules to simplif and then solve these equations. 7. log log log 8. log 9. log log IV. For the function below find f b g. f bg. V. Write the equation of the circle described or pictured.. The center is (, -) with a radius of cm.. Use the picture to find the equation 9
VII. OIT s: Answer each question.. Find the equation of the line that goes through (, -) and (, ).. Simplif the following epressions, without using a calculator (These were problems on the AP Calculus test) a. 8 cos 8 cos b. cos e #, #, & #: Limits, Limits, and more Limits I. Solve the following limits analticall. DO NOT USE A CALCULATOR!. lim. lim 6. lim 6. lim. lim 6. lim 7. lim
8. lim 9. lim. lim. lim 8. lim. lim. a. lim b. lim c. lim. a. lim b. lim c. lim 7. a. lim ln b. lim ln c. lim ln
8. a. lim h b g b. lim h h h b g h h 9. a. lim h b g b. lim h h 8 h b g h h II. Mark each statement as true (T) or false (F) in the net two problems...
III. Use our calculator to fill in the tables below and then estimate the limit to three decimal places.. If fbg sin then lim sin X f ( ) X f ( ). -.. -.. -.. -.. If f b g sin then lim sin X f ( ) X f ( ). -.. -.. -.. -. IV. Solve the following limits analticall.. lim 7. lim 6 6. lim 8 7. lim 8. lim sin 9. lim cos F HG F H G I K JI KJ. lim 68 a f. lima sin f
Fill in the following chart with the eact trig values at each angle measurement. Remember the following definitions for our trig. functions. opp. adj.. sin A cos A tan A opp hpot. hpot. adj.. csc A hpot. sec A hpot. cot A adj opp. adj. opp. Degree 6 9 8 7 6 Radian 6 Sin 7 7 6 6 6 Cos Tan Csc Sec Cot