Module 4 Test

End Behavior and Domain and Range of Polynomials

100

Where is this function going as x goes to the left?

f(x) = -3x⁴

- infinity

200

Where is this function going as x goes to the right?

f(x) = 3x + 1

infinity

300

What is the domain of f(x) = 4x³ + 2?

All real numbers

400

What is the range of f(x) = 3x²?

y >= 0

500

Write the end behavior for this function?

f(x) = 3x³ - 2

As x to - infinity, y to - infinity.

As x to infinity, y to infinity.

Polynomial or Not

100

y = 10

yes

200

y = 2x² + 1/2

yes

300

y = 3x^-2 +4x^-1

no

400

y = 1/x + 3

no

500

Name three examples of expressions that are NOT polynomials.

answers vary

Find Zeros of Polynomials

100

Find the zeros.

y = x² - 4

-2, 2

200

Find the zeros. Round to three decimal places.

y = 3x³ - 16

~1.747

300

Find the zeros. Round to three decimal places.

y = 4x⁴ - 16

~-1.414, 1.414

400

Find the zeros.

y = 3x²

0

500

Name two other names for zeros of a polynomial.

Roots, x-intercepts

Add and Subtract Polynomials

100

Add.

(2x² + 3x + 2) + (3x² - 5x - 1)

5x² - 2x + 1

200

Add.

(2x³ + 4x² - 3x + 1)+(5x² + 2x - 1)

2x³ + 9x² - x

300

Subtract.

(3x + 2) - (4x - 2)

-x + 4

400

Subtract.

(3x² - 5x + 5) - (6x + 2)

3x² - 11x + 3

500

Add.

(4x + 4 - 12x² - 11x⁴) + (3x² - 5x -10 + 6x³)

-11x⁴ + 6x³ - 9x² - x - 6

Multiply and Divide Polynomials

100

Multiply.

3x⁶(4x²)

12x⁸

200

Multiply.

(9x + 4)(2x - 1)

18x² - x - 4

300

Divide.

(x³ + 3x² - 28x - 62)/(x + 6)

x² - 3x - 10 - 2/(x+6)

400

Divide.

(a³ - 4a² +5a - 55)/(a - 5)

a² + a + 10 - 5/(a - 5)

500

What is the remainder?

(-4x² - 24 + x⁴ - 9x)/(x + 2)

-6