1. The sum or difference of monomial functions. (Exponents are non-negative.) f(x) = a n x n + a n-1 x n-1 + … + a 0 Degree of the polynomial is the degree of the highest degree term. Leading coefficient is a n. The graph is a smooth and continuous. The domain is all real numbers.

2. Graph these: y = (x – 4) 4 + 2 y = -(x+ 3) 5

3. For any polynomial f(x) = a n x n + … If n is odd a) and a > 0, then the graph rises from left to right b) and a< 0, then the graph falls from left to right If n is even a)and a> 0, then the graph rises on both ends b)and a< 0, then the graph falls on both ends

4.  Match the equations to the pictures on the board. f(x) = -x 3 + 4x f(x) = x 4 – 5x 2 + 4 f(x) = x 5 – x Describe the end behavior using limit notation.

5.  If f(x) = a n x n + … How many real zeros does f(x) have? At most n. How many turning points (where it changes from increasing to decreasing vice versa) does f(x) have? At most n-1.

6.  x = a is a zero of the function f.  x = a is a solution or root of the equation f(x) = 0.  (x – a) is a factor of f(x).  (a,0) is an x-intercept of the graph of f.

7.  f(x) = x 3 – x 2 – 2x  f(x) = -2x 4 + 2x 2  f(x) = x 3 + 3x 2 – 4x – 12  f(x) = x 4 – 10x 2 + 9 (this is in quadratic “form”)  f(x) = (x + 1) 3 (x – 2) 2 (note the effect of the mutiplicity of the roots) Consider end behavior, y-intercepts, zeros (and their multiplicity).

8. Go into CATALOG and turn your DIAGNOSTIC ON. Make sure your STAT PLOT is on. Enter data by going into STAT then EDIT. Set an appropriate WINDOW. Go into STAT then CALC. Pick an appropriate model. Go to Y= and then VARS, STATISTICS, EQ to paste your equation to graph. Check the value of R 2 to see if your equation is a good fit. Some calculators made need to change MODE to CLASSIC.

9. Review of 2.1 1. Solve 5(x+1) 3/2 = 40 2. Solve 1 + √(x-1) = x 3. Graph y = 7x -2 4. Graph y = x 2/3

10. 1. Solve 3x(7x - 2)(x 2 – 5)(x 2 + 4) = 0 2. Graph f(x) = -2x 4 + 16x 2 + 18 3. Graph f(x) = x 2 (x-2) 3 (x+ 1)

11. 1. Write a function with roots 2, 2, -3, and 0. 2. Write a cubic function with zeros only at 1 and 2. 3. Write a quartic equation with roots only at 1 and 2 and no multiple roots.