Attn: Upcoming Functions Analtic Geometr students, All Functions Analtic Geometr students should complete this assignment prior to the first da of class. During the first week of school, time will be spent answering questions students ma have on the material covered in this packet with the understanding that the will be assessed on these topics starting the second week of school and throughout the ear. This review will be in addition to covering new material from the first chapter, Functions and Their Graphs. Functions Analtic Geometr is a one-ear preparator course for AP Calculus BC. This course is designed for students who have successfull completed the standards for Pre AP Algebra II /Trigonometr. Throughout the ear students will learn various objectives which will challenge them and will help to enhance their problem solving skills. This packet was devised to help students be successful not onl in Functions Analtic Geometr but in all subsequent math courses as one of the goals of this class is to prepare students for the challenge of AP studies in mathematics. It is essential for students to master the skills covered in this packet. You must be able to understand and appl this information throughout the school ear. To best prepare for this class, it is recommended that students complete this packet within two to three weeks directl before school starts. Calculators should not be used to complete this packet. If some concepts are challenging and require a refresher of the material, two good sites for information are www.khanacadem.org and www.purplemath.com. If ou have questions regarding the nature of this course, the summer assignment or anthing else, please feel free to email me. In the summer I usuall check m email once a week. I will respond as soon as possible. Good luck! Enjo our summer vacation! I look forward to meeting ou in the fall! Ms. Modica modicalm@pwcs.edu
Section - FACTORING Factor the following problems. a. 7 8 b. n n + c. n 6 n + 9 d. f ( ) e. f ( ) 0 f. + 8 h. 7³ + 8 i. a 7 j. 8-5
Solve each quadratic equation b completing the square. a. 6 0 b. 7 0 c. 0 d. 6 7 0
Section - FUCNTIONS Use the information in the bo below to answer questions parts a h below. Given the following functions: f ( ) g( ) 5 m ( ) 5 n ( ) h ( ) 5 j ( ) k ( ) Find each of the following composed functions and state the domain: a. h f ( ) b. j n( ) c. n f ( ) d. f g( ) e. f m( ) Find the inverse of: f. f() g. g() h. n() For the following pairs of functions show that ( f g)( ) ( g f )( ) i. f ( ) ; g( ) j. f ( ) ; g( ) k. f ( ) a b ; g( ) ( b) a l. f ( ) 7 ; 7 g ( )
Section POLYNOMIALS, RATIONALS, EXPONENTIALS and LOGARITHIMS Simplif. a. 7 0 6 8 b. 6 6 6 c. d. 8 6 6 5 6 5 5 g. ( ) 7 h. 5 ( r s )( r s ) i. 6 j. 0 k. 5 a b ab 5 b a l. ( 5 )( a b ) m. 8 n. 5 9 z o. 56 z p. 9 65 z q. 9 6 ( 6 ) r. 6 0 5 (6 ) Evaluate each epression. a. 5 b. 8 c. (00 ) d.
Indicate our answer below b circling the best response. a. What is log a written in eponential form? (a) = a (b) a = (c) a = (d) a = b. The equation = a epressed in logarithmic form is: (a) (b) (c) (d) log a a log log log c. The epression log is equivalent to: a a (a) log + log (b) log 6 + log 6 (c) log log (d) log log d. The epression log is equivalent to: (a) log (b) log + log (c) (log )(log ) (d) log e. The epression to: a log b loga (a) logb (b) (loga logb) (c) (loga logb) (d) loga logb is equivalent f. The epression loga logb is equivalent to: (a) log( a b) (b) log a b log a logb (c) (d) log ab g. Which of the following equations is equivalent to log 7log log5? (a) 7 5 (b) ( 7) 5 7 (c) 5 (d) 5
Solve each equation. a. log log log g. 6 6 6 b. 9 h. log log log log c. i. ln 5 ln ln d. log 8 j. ln ln ln ln e. log 5 8 k. log 6 log log f. 5 5 l. log log
Section EXPONENTIAL, LOGARITHMIC, NATURAL LOG and e GRAPHS Create a table of values for the parent graph, graph (remembering transformations), and state the domain, range and asmptote for each of the following: - - - 0 a. b. c. d. D: D: D: D: R: R: R: R: Asmptote(s): Asmptote(s): Asmptote(s): Asmptote(s): - - - 0 Hint (logarithm function is the inverse of an eponential function) e. f. log log g. log ( ) h. log D: D: D: D: R: R: R: R: Asmptote(s): Asmptote(s): Asmptote(s): Asmptote(s):
FA 6-7 - - - 0 i. e j. e k. e l. e D: D: D: D: R: R: R: R: Asmptote(s): Asmptote(s): Asmptote(s): Asmptote(s): Hint (logarithm function is the inverse of an eponential function - - 0 m. ln n. ln( ) o. ln p. ln( ) D: D: D: D: R: R: R: R: Asmptote(s): Asmptote(s): Asmptote(s): Asmptote(s):
Section 5 TRIGONOMETRY Fill in the values of the unit circle below: In the ovals write the degree value In the rectangles write the radian value In the parentheses write the coordinate value
Using the unit circle, fill in the information below: Degrees Radians sine cosine tangent cosecant secant cotangent 0 0 5 60 90 0 5 50 80 0 5 0 70 00 5 0 60
Graph the following trig functions. a. sin per: amp: b. cos amp: per:
c. tan amp: per: Solve each triangle b finding all of the missing side lengths and angle measures using the Law of Sines and/or the Law of Cosines. (A calculator ma be used to answer these questions). d. e. Q C 8 P 8 0 M B 5 D f. F 6 0 0 G H