This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Polynomial Function A polynomial function is a function that can be written in the form , where are real numbers and n is a nonnegative integer. Basically it is a function whose rule is given by a polynomial in one variable. If you need a review on functions, feel free to go to Tutorial 30: Introduction to Functions . If you need a review on polynomials in general, feel free to go to Tutorial 6: Polynomials. An example of a polynomial function is . Leading Term When the polynomial function is written in standard form, , the leading term is . In other words, the leading term is the term that the variable has its highest exponent. The leading term of the function would be . Leading Coefficient When the polynomial function is written in standard form, , the leading coefficient is . Basically, the leading coefficient is the coefficient on the leading term. The leading coefficient of the function would be  4. Degree of a Term of a Polynomial Function The degree of a term of a polynomial function is the exponent on the variable. Degree of a Polynomial Function When the polynomial function is written in standard form, , the degree of the polynomial function is n . The degree of the polynomial is the largest degree of all of its terms. The degree of the function would be 7. The Leading Coefficient Test There are four cases that go with this test: Given a polynomial function in standard form : If n is odd AND the leading coefficient , is positive , the graph falls to the left and rises to the right : Case 2: If n is odd AND the leading coefficient , is negative, the graph rises to the left and falls to the right. Example 1 : Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial . First question is what is the leading term? If you said , you are correct!! Second question is what is the leading term’s degree? If you said 3, you are right on!! 3 is the exponent on the leading term, which also means it is the degree of the polynomial. Third question is what is the coefficient on the leading term? If you said 5, pat yourself on the back!! Putting this information together with the Leading Coefficient Test we can determine the end behavior of the graph of our given polynomial: Since the degree of the polynomial, 3, is odd and the leading coefficient, 5, is positive, then the graph of the given polynomial falls to the left and rises to the right. Example 2 : Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial . First question is what is the leading term? If you said , you are correct!! Second question is what is the leading term’s degree? If you said 4, you are right on!! 4 is the exponent on the leading term, which also means it is the degree of the polynomial....
View
Full
Document
This note was uploaded on 02/18/2011 for the course MATH 101 taught by Professor Kindle during the Spring '11 term at South Texas College.
 Spring '11
 Kindle
 Algebra, Real Numbers

Click to edit the document details