Lesson Overview:

 

• End behavior of polynomial functions

• Use Sign Diagrams to sketch the polynomial functions

 

Part A: Finding the end behavior of the polynomial function:

These videos teach how to graph Piecewise and Step Functions:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Above are the end behaviors of all leading coefficients. These end behaviors only describe x as it approaches infinity and negative infinity and does not describe the entire function. Now let’s practice using the leading coefficient to find the end behavior of polynomial functions.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The leading term of this polynomial function is 3x4 which has a positive coefficient and an even degree. This means we look at the top left box to find the end behaviors of this polynomial function.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The leading term of this function is -5x6 which has a negative coefficient and an even degree. In this example, we look at bottom left box find the end behaviors of this function.

 

Using sign diagrams to sketch polynomial functions:

Steps:

• Find the leading term and end behavior of a polynomial function

• Find the real zeros

• Use sign diagram to draw a rough sketch of the graph

Video:

 

 

 

 

 

 

 

 

 

 

 

End Behavior in Test Questions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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The answer is B because the leading term has a negative coefficient and an odd degree.

 

Real World Connection of Sign Diagram

 

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By using a sine graph you can likely predict the ups and downs of the roller coaster, but because the roller coaster travels in a loop is it likely impossible to find the end behavior.

 

 

Conclusion:

In conclusion, you can use Cosine Law to solve for triangles when you are lacking one side or one angle. Make sure you label your triangle appropriately and to remember that your calculator is your best friend. You can use Sine Law to solve for triangles by knowing two sides and one angle or two angles and one side. Simply plug in the appropriate numbers into the formula and solve. It is important to keep in mind that sometimes it may be necessary to use Sine Law along with Cosine Law to solve for a triangle.