POLYNOMIAL & RATIONAL FUNCTIONS (1.6)
NAME_______________________________
1. Consider the function y( x)  x6  2 x5  8x 4  14 x3  11x 2  28 x  12
A. Plot y ( x) in the window 3  x  4 , 50  y  100 .
-3
-2
-1
0
1
2
3
4
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  8w0.25 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.
(i) y 
25 x  2
5 x3  1
(ii) y 
25 x  6 x 2
2 x 2  10
(iii) y 
4 x2
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
4
1.5
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