Polynomials - Notes PDF

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POLYNOMIAL & RATIONAL FUNCTIONS (1.6)

NAME_______________________________

1. Consider the function y( x)  x6  2 x5  8 x4 14 x3 11x2  28x 12 A. Plot y ( x) in the window  3  x 4 ,  50  y 100 .

B. Find the zeros of y ( x) .

C. Express y ( x ) in factored form.

2. Create a possible equation for the polynomial graphed below. Include the sign of the leading coefficient.

-6 -5 -4 -3 -2 -1 0

1

2

3

4

3. Solve for h as a function of s and simplify:

5

s 8 w0.25 h0.75

4. Create equations of rational functions with the following characteristics: A. A horizontal asymptote of y 2 and a vertical asymptote of x 4 .

B. No horizontal and no vertical asymptotes.

5. Match the function expressed in words with a graph and an equation. Find the horizontal asymptote for each, A. Average cost of producing x items. B. The oxygen content in a lake after dumping in fertilizer as a function of time. (The oxygen content decreases at first, but then returns to its previous level.) C. The amount of a drug in a body as a function of time. (Assume the drug was given by injection.) D. The number of people purchasing a (trendy) new product as a function of time. E. The number of people getting a particular disease during an epidemic as a function of time.

25 x  6 x2 2 x 2  10

25 x  2 5x 3  1

(i) y 

(ii) y 

(iii) y 

4x 2 x2  9

(iv) y 

a.

b.

5

1.2

4

1

3

0.8

2

0.6

1

0.4

20 x 1000 x

(v ) y 

x2  x  1 x2 1

0.2

0 0

10

20

30

40

50

60

0

x

0

c.

2

4

6

8

10

d. 10

4.5 4

8

3.5 3

6

2.5 2 1.5

4

1

2

0.5 0

0 0

5

10

15

20

25

0

30

1

2

e. 1000 800 600 400 200 0 0

5

10

15

20

25

30

3

4...