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 → +∞.

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 → +∞.

EXAMPLE 6

The energy E (in foot-pounds) in each square foot of a wave is given by the model E = 0.0029s4 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

Solve a multi-step problem

EXAMPLE 6 Solve a multi-step problem

SOLUTION

Make a table of values. The model only deals with positive values of s.

STEP 1

EXAMPLE 6 Solve a multi-step problem

STEP 2 Plot the points and connect them with a smooth curve. Because the leadingcoefficient is positive and the degree iseven, the graph rises to the right.

STEP 3 Examine the graph to see that s 24 when E = 1000.

The wind speed needed to generate the wave is about 24 knots.

ANSWER

GUIDED PRACTICE for Examples 5 and 6

Graph the polynomial function.

9. f(x) = x4 + 6x2 – 3 10. f(x) = –x3 + x2 + x – 1

GUIDED PRACTICE for Examples 5 and 6

11. f(x) = 4 – 2x3

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 = 0.0051s4. 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.