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Lesson 12-filled-2

# Lesson 12-filled-2 - Math 1314 Lesson 12 Curve Sketching...

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Lesson 12 Curve Sketching One of our objectives in this part of the course is to be able to graph functions. In this lesson, we’ll add to some tools we already have to be able to sketch an accurate graph of each function. From prerequisite material, we can find the domain, y -intercept and end behavior of the graph of a function, and from the last two sections, we can learn much about a function by analyzing the first and second derivatives. We also know how to find the zeros of some functions. We’ll expand that group of function before we continue to curve sketching. The Rational Zeros of a Polynomial Function The rational zeros of a function are the zeros of the function that can be written as a fraction, such as 2 or . 5 1 - We can find all of the possible rational zeros of a given function using the Rational Zeros Theorem. Then we can use synthetic division to determine which – if any – of the possible rational zeros are actual zeros of the function. Here’s the theorem: Rational Zeros Theorem: Suppose 0 1 1 ) ( a x a x a x f x n n n + + + = - - , where 0 n a and 0 0 a , and all of the coefficients of the polynomial are integers. If q p x = is a rational zero of the function, where p and q have no common factors, then p is a factor of the constant term 0 a and q is a factor of the leading coefficient n a . Example 1

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Lesson 12-filled-2 - Math 1314 Lesson 12 Curve Sketching...

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