Pre-Calculus/Trig Name: __________________________ Unit 2 ReviewDate: _______________ Block: ______ Directions: Complete all work on a separate piece of paper. III. Identify the end behavior of each function, without referencing a graphing calculator. IV. Given the following zeros, find all of the linear factors and the least degree polynomial function. V. For each polynomial (#1, 2, 3) complete the following: a)Use the leading coefficient test to describe the end behavior b)Use the rational root test to determine all possible roots. Use Descartes rule of signs to determine how many positive and negative real zeros there are. (*Don’t forget if you notice an upper or lower bound it is helpful, but not necessary) c) Use synthetic division to determine all zeros. d) Graph the polynomial (WITHOUT A CALCULATOR). This means you will not need to have exact mins/maxs. (Use end behavior and roots to shape your graph!) 1.) f(x) = x 3 -5x 2 -8x+12; given (x+2) 2.) f(x) = 2x 4 +7x 3 -4x 2 -27x-18; given: (x-2),(x+3) 1.) f(x) = 3x 3 +2x 2 -19x+6 2.) f(x) = 2x 3 + 3x ) f(x) = 5-2x-3x 2 2.) y=2x 5 -5x+73. g(x) = -x 3 +2x 2 +3x-4 1.) x={4, -3, 1}2.) x= {0 mult. 3, -5, 7}3. x= {2, -5, -4i, 4i} (a)Describe End Behavior: As x  - , f(x)  ____. As x  , f(x)  ____. (b) Possible Zeros: _______________________ # of Positive Real Roots: _________________ # of Negative Real Roots:_________________ (c) Zeros: ______________________________ (a)Describe End Behavior: As x  - , f(x)  ____. As x  , f(x)  ____. (b) Possible Zeros: _______________________ # of Positive Real Roots: _________________ # of Negative Real Roots:_________________ (c) Zeros: ______________________________ I.Write the equation for the polynomial that would give the following roots. Sketch a graph of it (Accurate max/min don’t have to be on there!!) 1.) x= -5, 0 multiplicity 3, 7, leading coefficient >0 2.) x = -9, 2, -5, 8 double root, leading coefficient < 0

**Follow directions on front for #3!!! 3.) f(x) = x 4 +9x 3 +28x 2 +36x+16 4.) f(x) = -x 3 +7x+6 5.) f(x) = -x 3 +3x 2 -4x+26.) f(x) = x 3 -x 2 -13x-3 7.) f(x) = x 3 +x 2 +4x+48.) f(x) = -x 4 +4x 2. VI. For each polynomial (#4-8) complete the following: a)Use the leading coefficient test to describe the end behavior b)Use the rational root test to determine all possible roots. Use Descartes rule of signs to determine how many positive and negative real zeros there are. (*Don’t forget if you notice an upper or lower bound it is helpful, but not necessary) c) Use synthetic division to determine all zeros. d) Use your graphing calculator to find all relative maxima and minima. e) Describe the intervals over which the polynomial is increasing and decreasing. f) Sketch the graph of the polynomial. You must include the y-intercept, all zeros, min(s)/max(s) and the basic shape using the Leading Coefficient Test. (a)Describe End Behavior: As x  - , f(x)  ____. As x  , f(x)  ____. (b) Poss. Zeros: _______________________ # of + Roots:______ # of – Roots:______ (c) Zeros:________________________ (d) Min/Max:______________________ (e) Increasing:_________Decreasing:________ (a)Describe End Behavior: As x  - , f(x)  ____. As x  , f(x)  ____. (b) Possible Zeros: _______________________ # of Positive Real Roots: _________________ # of Negative Real Roots:_________________ (c) Zeros: ______________________________ (a)Describe End Behavior: As x  - , f(x)  ____. As x  , f(x)  ____. (b) Poss. Zeros: _______________________ # of + Roots:______ # of – Roots:______ (c) Zeros:________________________ (d) Min/Max:______________________ (e) Increasing:_________Decreasing:________ (a)Describe End Behavior: As x  - , f(x)  ____. As x  , f(x)  ____. (b) Poss. Zeros: _______________________ # of + Roots:______ # of – Roots:______ (c) Zeros:________________________ (d) Min/Max:______________________ (e) Increasing:_________Decreasing:________ (a)Describe End Behavior: As x  - , f(x)  ____. As x  , f(x)  ____. (b) Poss. Zeros: _______________________ # of + Roots:______ # of – Roots:______ (c) Zeros:________________________ (d) Min/Max:______________________ (e) Increasing:_________Decreasing:________ (a)Describe End Behavior: As x  - , f(x)  ____. As x  , f(x)  ____. (b) Poss. Zeros: _______________________ # of + Roots:______ # of – Roots:______ (c) Zeros:________________________ (d) Min/Max:______________________ (e) Increasing:_________Decreasing:________