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Polynomial Function Graphing Guide

Learn how to graph polynomial functions step by step. Understand end behavior, make tables of values, and connect points to create smooth curves. Examples and solutions provided for better understanding.

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Polynomial Function Graphing Guide

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  1. 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. EXAMPLE 5 Graph polynomial functions Graph (a)f (x) = – x3 + x2 + 3x – 3 and (b)f (x) = 5 x4 – x3 – 4x2 + 4. SOLUTION The degree is odd and leading coefficient is negative. So, f (x) → + ∞ asx → –∞ andf (x) → –∞ asx → + ∞.

  2. b. 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. EXAMPLE 5 Graph polynomial functions The degree is even and leading coefficient is positive. So, f (x) → ∞asx → –∞and f (x) → ∞asx → + ∞.

  3. Physical Science The energy E (in foot-pounds) in each square foot of a wave is given by the model E = 0.0029s4 where sis 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. EXAMPLE 6 Solve a multi-step problem

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

  5. 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 24 when E = 1000. The wind speed needed to generate the wave is about 24 knots. ANSWER EXAMPLE 6 Solve a multi-step problem

  6. Graph the polynomial function. 9. f (x) = x4 + 6x2– 3 x – 2 –1 0 1 2 y 374 –3 4 37 for Examples 5 and 6 GUIDED PRACTICE 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.

  7. x – 3 –2 –1 0 1 2 y 409 0 –1.7 –3 2 for Examples 5 and 6 GUIDED PRACTICE 10.f (x) = 2x3 + x2 + x – 1 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.

  8. 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. x – 2 –1 0 1 2 y 206 4 –12 2 for Examples 5 and 6 GUIDED PRACTICE 11. f (x) = 4 – 2x3 SOLUTION

  9. 12. 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? ANSWER about 25 mi/h. for Examples 5 and 6 GUIDED PRACTICE

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