1. EXAMPLE 5
Graph polynomial functions
Graph (a) f (x) = –x3 + x2 + 3x – 3 and (b) f (x) = x4 – x3 – 4x2 + 4.
SOLUTION
To graph the function, make a table of values and plot the corresponding points. Connect the points with a smooth curve and check the end behavior. a.
The degree is odd and leading coefficient is negative. So, f (x) → +∞ as x → –∞ and f (x) → –∞ as x → +∞.

2. EXAMPLE 5
Graph polynomial functions
To graph the function, make a table of values and plot the corresponding points. Connect the points with a smooth curve and check the end behavior. b.
The degree is even and leading coefficient is positive.
So, f (x) → +∞ as x → –∞ and f (x) → +∞ as x → +∞.

3. EXAMPLE 6
Solve a multi-step problem
The energy E (in foot-pounds) in each square foot of a wave is given by the model E = s4 where s is the wind speed (in knots). Graph the model. Use the graph to estimate the wind speed needed to generate a wave with 1000 foot-pounds of energy per square foot.
Physical Science

4. EXAMPLE 6
Solve a multi-step problem
SOLUTION
Make a table of values. The model only deals with positive values of s.
STEP 1

5.  EXAMPLE 6 Solve a multi-step problem STEP 2
Plot the points and connect them with a smooth curve. Because the leading
coefficient is positive and the degree is
even, the graph rises to the right.
STEP 3
Examine the graph to see that s when E = 1000. 
The wind speed needed to generate the wave is about 24 knots.
ANSWER

6. GUIDED PRACTICE
for Examples 5 and 6
Graph the polynomial function.
9. f(x) = x4 + 6x2 – 3
10. f(x) = –x3 + x2 + x – 1

7. GUIDED PRACTICE
for Examples 5 and 6
11. f(x) = 4 – 2x3

8. GUIDED PRACTICE
for Examples 5 and 6
WHAT IF? If wind speed is measured in miles per hour, the model in Example 6 becomes
E = s4. Graph this model. What wind
speed is needed to generate a wave with 2000 foot-pounds of energy per square foot?
12.
ANSWER
about 25 mi/h.