1

2

Graphing Polynomials

W-Substitutions

Roots and Zeros

Operations on Functions

Inverse Functions

100 100 100 100 100

200 200 200 200 200

300 300 300 300 300

400 400 400 400 400

500 500 500 500 500

3

Graphing Polynomials100

• Find the x and y-intercepts of the function P(x) = x4 – 4x2 – 5.

4

Graphing Polynomials200

• Find the x and y-intercepts of the function y = 2x3 – 5x2 + 3x.

5

Graphing Polynomials300

• Determine the end-behavior of the following polynomials: (a) y= -x4 – 4x2 + 4

(b) y = 2x3 – x + 3

6

Graphing Polynomials400

• Graph the polynomial P(x) = x3 – 3x2 – 4x + 12. Label the intercepts.

7

Graphing Polynomials500

• Graph the polynomial P(x) = -x3 – 3x2 + 9x + 27. Label the intercepts.

8

W-Substitutions100

• Solve for x using quadratic substitution. Check.

€

x − 3 x = −2

9

W-Substitutions200

• Solve for x using quadratic substitution. Check. If you use the decimal version of the solution, round to three decimal places.

€

(x + 3)6 − 4(x + 3)3 − 21 = 0

10

W-Substitutions300

• Solve for x using quadratic substitution. Check.

€

3(2x −1)4 − (2x −1)2 − 2 = 0

11

W-Substitutions400

• Solve for x using quadratic substitution. Check.

€

1

x +1

⎛

⎝ ⎜

⎞

⎠ ⎟2

− 41

x +1

⎛

⎝ ⎜

⎞

⎠ ⎟− 5 = 0

12

W-Substitutions500

• Solve for x using quadratic substitution. Check.

€

x −1( )1/ 2

− (x −1)1/ 3 − 4(x −1)1/ 6 + 4 = 0

13

Roots and Zeros100

• Write the simplest polynomial with zeros 2, -3, and -2.

14

Roots and Zeros200

• Write the simplest polynomial with zeros i and .

€

2

15

Roots and Zeros300

• Use Descartes Rule of Signs to determine the possible number of positive, negative, and imaginary solutions of f(x) = x5 – x4 + 3x3 + 9x2 – x + 5.

16

Roots and Zeros400

• Use Descartes Rule of Signs to determine the possible number of positive, negative, and imaginary solutions of f(x) = x5 + x4 + 4x3 + 3x2 + x + 1.

17

Roots and Zeros500

• Write the simplest polynomial with zero 4 – i.

18

Operations on Functions100

• Use the functions f(x) = 2x – 1, g(x) = x2, and

to compute the following:

(a) (fg)(-2)

(b) (f+h)(4)

(c) g(h(0))

€

h(x) = x − 6

19

Operations on Functions200

• Use the functions f(x) = 2x – 1, g(x) = x2, and

to compute the following:

(a) (fg)(x)

(b) f(g(x))

(c)

€

h(x) = x − 6

€

(h og)(x)

20

Operations on Functions300

• Use the functions f(x) = 5x, g(x) = 3x + 2, and h(x) = 6x2 + x – 2 to compute the following:

(a)

(b) f(g(x))

€

h

g

⎛

⎝ ⎜

⎞

⎠ ⎟(x)

21

Operations on Functions400

• Use the functions f(x) = 5x, g(x) = 3x + 2, and h(x) = 6x2 + x – 2 to compute the following:

(a) (gh)(x)

(b)

(c) f(f(-1))

€

f oh( )(1)

22

Operations on Functions500

• Use the functions f(x) = 2x – 1, g(x) = x2, and

to compute f(g(h(g(2)))).

€

h(x) = x − 6

23

Inverse Functions100

• Find the inverse of f(x) = 2x – 8.

24

Inverse Functions200

• Find the inverse of .

€

f (x) =1

7x − 3

25

Inverse Functions300

• Find the inverse of .

€

g(x) = 2x − 64

26

Inverse Functions400

• Find the inverse of .

€

h(x) =4x − 3

2x + 4

27

Inverse Functions500

• Find the inverse of the function .

€

f (x) =1− x3

1+ x3