Unit 2 Review. No Calculator Allowed. 1. Find the domain of each function. (1.2)

Transcription

1 PreCalculus Unit Review Name: No Calculator Allowed 1. Find the domain of each function. (1.) log7 a) g 9 7 b) hlog7 c) h 97 For questions &, (1.) (a) Find the domain (b) Identif an discontinuities as removable or non-removable. (c) Find an equations of vertical asmptote(s) and/or holes (as ordered pairs) g h 9 4. Describe the end behavior of the function below using limit notation. (1.) a) b) For questions 5, complete the following: (1. and 1.5) (a) Identif the parent function (c) Identif the domain and range and (b) Describe the transformation. (d) Accuratel graph each function. 5. f( ) log. 4

2 Graph each piecewise function. (1. and 1.5) 1 if 7. f( ) if if 1 f( ) 1 if 1 Write the equation of the piecewise function shown below. (1. and 1.5) Graph each function without a calculator. State the (a) amplitude, (b) period, (c) phase shift and (d) vertical shift. Label each ais. (Graphing Trig. Functions) π = 5cos 4 1. = cos 11. ( ) 1. ( π ) = sin Write the equation(s) of the cosine function with amplitude 5, period π, phase shift π, and vertical shift of 1.

3 15. Write the equation of the function shown below using the given parent function (Graphing Trig. Functions) a) = sin b) = cos 1 π/8 π For questions 1-17, use limit notation to describe the end behavior of each polnomial. (-) 1. 5 f( ) = f 4 ( ) = + 10 For each function in questions 18-19, list the degree, state each zero and its multiplicit, and then graph each polnomial. Note a scale on the -ais. (-) 18. f( ) ( 4) ( 1) = f = + ( ) 18 7 For questions 0-, determine (if it eists): (-7) a) end behavior including HA or Slant Asmp. d) -intercept b) vertical asmptotes e) graph (with enough points to be accurate or a sign chart) c) -intercept(s) = 1 1. = 8 4. =

4 Graphing Calculator Allowed *******KNOW THE 1 PARENT FUNCTIONS AND THEIR PROPERTIES BE ABLE TO ANSWER QUESTIONS LIKE THOSE ON YOUR WORKSHEET 1.. For each function below, prove algebraicall whether the function is even, odd, or neither. (1.) 4. f 7 4. f ( ) = 4 Using our calculator, graph the function f 5 4and (1.) 5. State the intervals on which the function is increasing and decreasing.. a) Find all relative etrema. b) Find an absolute etrema or eplain wh there are none. 7. Given g () = and f () = 8, find g ( f ( )). (1.4) For questions #8-5, suppose f () = 7 and g () =. Find each of the following AND state the domain of the new function. (1.4) 8. f g 9. fg 0. f g 1 1. f g. g ( f ()). f 4. reflection of f () over the -ais. 5. reflection of g () over the -ais.

5 . For each of the following, (1.4) i) Find the inverse of the function. ii) VERIFY that the function is an inverse b using the definition of inverse functions. a) f 4 = + b) h 5 ( ) 4 7. Are the given graphs functions? Eplain wh or wh not. Do the have an inverse that is also a function. Eplain wh or wh not? a) b) Can ou transform all the parent functions and graph them using correct points? Can ou graph a piecewise function? Can ou write the piecewise equation for a given graph? Can ou find the domain without a calculator remembering the domain issues presented in this chapter? Can ou find (and tell the difference between) a vertical asmptote and a hole in a function when given the equation? Can ou describe end behavior of a function using limit notation? Can ou state the multiplicit of the zeros of a polnomial given the factored form? Can use the multiplicit of the zeros and the end behavior of a polnomial to sketch the graph of the function? Can ou find horizontal asmptotes of rational functions? Can ou find slant asmptotes? Can ou use the function notation to add/subtract/multipl/divide functions? Can ou use composite function notation? Can ou prove whether a function is odd, even or neither? Can ou find an inverse of an equation? Can ou prove two equations are inverses and know the difference between proving and finding inverses? Can ou correctl describe when a function is increasing or decreasing? Can ou correctl find and describe the etrema of a function? Can ou eplain the difference between absolute and relative (local) etrema? Can ou use the terms, bounded, bounded above, and bounded below correctl? Can ou describe the difference between removable and non-removable discontinuities? Unit 1 Review (Yeah anthing from Unit 1 could be on the Unit Eam too!) REVIEW YOUR WORKSHEETS, QUIZZES, AND NOTES and don t forget about that 1. WS specificall!