Math 3 Hon: Unit 3 Review Name: _________________________

I. Use the function 82923)( 234 ����� xxxxxf a. What is the leading coefficient? a. ________________________________

b. What is the degree of the polynomial? b. ________________________________

c. Find )2(�f c. ________________________________

d. Find all maximums and minimums: d. ________________________________

(label each as relative or absolute) ________________________________

e. Describe the end behavior: e. ________________________________

________________________________

II. Find if each binomial is a factor of the given polynomial.

1. Polynomial= 81023 ��� xxx Binomial = x + 1

2. Polynomial= 152852 23 ��� xxx Binomial = x – 5

III. Graph Interpretation

GRAPH #1:

a. State the number of REAL zeroes: ________ b. State the number of COMPLEX zeroes: ____ c. What is the possible degree? _____________ d. Is the leading coefficient positive or negative? e. What is the End Behavior?

GRAPH #2:

a. State the number of REAL zeroes: ________ b. State the number of COMPLEX zeroes: ____ c. What is the possible degree? _____________ d. Is the leading coefficient positive or negative? e. What is the End Behavior?

KEI3432

rel Max 1.06 1.93rel min 11 8.11 Abs Max 1.45 86Asx 70 y 7x i a yes

Yes b c remainder 0 Yes b c remainder O

6 4O 2

6

60 ox a y a

Xt o y s X o yX a y 2

GRAPH #3:

a. Degree? ___________

b. Leading Coefficient? _________

c. Identify all Maximums:

d. Identify All Minimums:

Use Interval Notation:

e. Where is the graph INCREASING?

f. Where is the graph DECREASING?

g. What is the RANGE of this graph?

GRAPH #4:

a. Degree? ___________

b. Leading Coefficient? _________

c. Identify all Maximums:

d. Identify All Minimums:

Use Interval Notation:

e. Where is the graph INCREASING?

f. Where is the graph DECREASING?

g. What is the RANGE of this graph?

IV. Find exact values of all zeroes.

1. 023 24 �� xx 2. 0376 24 �� xx

3. 8106 23 ��� xxx = 0 4. 𝑥3 + 3𝑥2 − 26𝑥 − 8 = 0

V. Sketch a possible graph of f(x) = - 4(x – 3)(x – 1)2(x + 5)3

0)(-7, 0)

(-5, 3)

(-2, 0)

(0, -4)

(3, -1)

(5, -6)

(6, 0) (-4, (0, 0)

(1, -10)

(4, -6)

(-3, 13)

5 4pos negC 5,3 3 1

o 4 5 63,13 4 6

I 10

C oo 5 0,35,007 C n 3 1,4

5,0 3,5 C 3 l 4 D

N N l 00213

1 2 211 417 0 3 2 1 2 2 3 0X2 2 2 1 X Iz X2 3 2x irz x Ii

x iy

Yl I 6 10 8 4J I 3 26 8

4 4 8 8 Itf2 2 2 F4 2

2 2 2 0 2 X 1 7 2 0

X 2trf4X 2

zX 7IFTz4

Af