1. Where am I now?
Review for quiz 4.1

2. Must have real coefficients & whole number exponents
1) Determine if the function is a polynomial function. If so, write in standard form and state degree, type, and leading coefficient
f(x) = ½x2 – 4x3 + 7 x4 – 3x How do you know when a function is a polynomial function?
f(x) = 7 x4 – 4x3 + ½x2 – 3x
4th; quartic; 7
Must have real coefficients & whole number exponents

3. 2) Write in standard form
f(x) = (x2 – 8x + 5)(4x – 3) How would you simplify: g(x) = (3x2 – 4x) – (8x + 1)
f(x) = 4x3 – 35x2 + 44x - 15
Distribute -1 through the second quantity

4. (4x – 3)3 How about: (4x + 3)3 64x3 – 144x2 + 108x - 27
3) Expand:
(4x – 3)3 How about: (4x + 3)3
64x3 – 144x x - 27
64x x x + 27

5. 4) Find the zeros and state any multiplicity:
f(x) = x(x – 10)6(x + 3)3
10 (mult 6)
-3 (mult 3)

6. 5) Write the polynomial function in standard form given the zeros…:
0, 0, -1, -1, 5
Start with: f(x) = x2(x + 1)2(x – 5)
f(x) = x5 – 3x4 – 9x3 – 5x2

7. 6) Given the function, answer the following:
f(x) = -x(x – 5)3(x + 6)4 Degree: Max # of turns: Max # of x-intercepts: Left behavior: Right behavior: Zeros: Sketch the function: 8 7 8
fall
fall
0, 5, -6

8. 7) Given the graph, answer the following:
Interval(s) of increase: Interval(s) of decrease: Where is y >0? Where is y < 0? Relative minimum: Relative maximum:
(-∞, -2) U (0.75, ∞)
(-2, 4)
(-2, 0.75)
(-3, -1) U (2, ∞)
(0.75, -8)
(-∞, -3) U (-1, 2) -8 4

9. I got it! I need a little help…
So, where are you????