Chapter 2 Quiz

What you need to know

• Chapter 2.1 – 2.31. The properties of a monomial function2. Properties of negative exponents3. Properties of rational exponents4. Ability to solve a radical equation5. Solve for the zeros of a polynomial function6. Know the basic properties of a polynomial function7. Ability to solve a long division problem8. Ability to verify a factor using synthetic division

Format

• Thursday December 9th

• 10 – 15 multiple choice questions

• 6 – 8 open ended questions

Identify properties of a polynomial function

• Which of the following graphs is not a polynomial function?

Properties of a polynomial

• -x34 + 400x23 – 7x2 + 400x + 3,000

• What is the degree?

34

• What is the coefficient?

-1

Analyze monomial functions• Graph and analyze 3x6

a. Domain (-∞,∞)

b. Range (0, ∞)

c. Intercept (0,0)

d. Symmetry – along the y axis

e. Continuous yes

f. Increasing/decreasing -, +

Analyze negative exponents• Graph and analyze 3x-2

a. Domain (-∞,0),(0,∞)

b. Range (0, ∞)

c. Intercept None

d. Symmetry – not applicable

e. Continuous no

f. Increasing/decreasing +, +

Solve Radical Equations

1. 3x = 3 + √18x – 182. 3x – 3 = √18x – 18 Subtract 3 from both sides

3. 9x2 – 18x + 9 = 18x – 18 square both sides

4. 9x2 – 36x + 27 = 0 subtract 18x, add 18

5. (3x – 9)(3x – 3) = 0 factor6. 3x – 3 = 0 →x = 1, 3x – 9 = 0 →x = 37. Verify 3(1) = 3 +√18(1) – 18 →3 = 3 yeah

3(3) = 3 +√18(3) – 18 → 9 = 9 yeah

What are the zeros of the polynomial

• X4 – 9x2 + 18

1. How many potential zeros?

4

2. How many potential bends?

33. How many zeros are listed on your calculator?

0 or unable to identify

4. What are the zeros?±√3 ±√6

Long division

• X3 + 2x2 – 21x + 18; x – 3• x2 + 5x - 6

x – 3 x3 + 2x2 – 21x + 18

x3 – 3x2

5x2 – 21x

5x2 – 15x

-6x + 18

-6x + 18

Factor x2 + 5x – 6 → (x + 6)(x -1)(x – 3)

Synthetic Division

• Determine whether x + 3 is a factor

X4 – 2x3 – 9x2 + x + 6

1. Solve for x: x + 3 = 0; x = -3

-3 1 -2 -9 1 6

-3 15 -18 51 (noooh

1 -5 6 -17