1 MAT146 Review for Exam I FALL 2011 EXAM I will cover Sections 1.8, 1.9, 2.2, 2.3, and 2.5. The exam will be given in class during the usual class time. There are NO make-up exams. Please be prepared to have your calculator cleared before and after the exam. You may not use a cell phone or any other device as a calculator. This review sheet is not meant to be a replica of the exam, but a guide for you to use when reviewing for the exam. All of these questions are from old exams. As always, please ask if you have any questions. 1. Find the quotient and remainder:42( 6 7 2) ( 1)x x x x    . 2. Is ( 1)x  a factor of 421xx? 3. List all zeros of the polynomial2( ) ( 4)( 2)P x x x  . 4. LIST all POSSIBLE rational roots of8 6 4 2( ) 2 3 5P x x x x x    . 5. Describe the end behavior of13 3( ) 8P x x x  . 6. For ()y f xshown below, answer questions a-d. You may assume that each tick mark represents one unit. y a. What are the roots of this polynomial? b. What happens as x ? c. Where is ( ) 0Px? Use interval notation. d. Write a possible equation for P(x). 7. Let 21( ) , ( )2f x x g xx. Find ( )( ),( )( )f g x g f x and the domain of each. x2 8. Use the information in the table below for (a), (b), and (c) below. x 3 2 1 0 1 2 3 ()fx 9 5 3 2 3 7 6 ()gx 9 3 0 1 2 4 10 a. ( )( 1)fg b. ( )(1)gf c. ( )(2)gg 9. Does 42( ) 3 1P x x x   have a root in ( 1, 3)? 10. Use interval notation to describe where( ) ( 7)( 12)( 5)( 10) 0P x x x x x     . 11. Given that 2( ) 4, 0f x x x   is a one-to-one function, find 1()fx and verify that the inverse is correct 12. Given that x = 3 is a root of 32( ) 9 26 24f x x x x   , factor completely and find all other real and/or complex roots. 13. True or false: a. For 32( ) ( 1) ( 2 1),f x x x x    x = -1 is a root with multiplicity 3. b. For 32( ) 2 5,f x x x   x= -1 is a root. c. 2( ) 2f x x is a one-to-one function. d. 3( ) 2 5f x x x   has a root in the interval [-2,5] 14. If 2( ) 4 3 7; ( ) 3 8f x x x g x x    , find ( )( )g f x. 15. Let ( ) 2 3f x xbe a one-to-one function. Without finding the inverse, give any point on the graph of the inverse function. 16. Use the graph of y = f(x) below to graph the inverse function. You may assume that each tick mark represents one unit. y = f(x) x y x y3 17. Given y = f(x) below, answer the following questions. Assume that each tick mark represents one unit. y = f(x) a. Find all roots and their multiplicities. b. What is the degree of this polynomial? c. How many turning points does this function have? d. Describe the end behavior. 18. For the graphs of f(x) and g(x) shown below, find: a.   0gf  0gf b.   1fg c.   3fg d.   0gf e.   2fg f.   2ff f(x): g(x): 19. If  263( ) , ( ) , find ( )f x x g x x f g x and the domain of the composite function. x