Section 5.1 Determine if a function is a polynomial function. State the degree of a polynomial function.
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4 Objectives Section 5.1 Section 5.1 Determine if a function is a polynomial function. State the degree of a polynomial function. Form a polynomial whose zeros and degree are given. Graph transformations (vertical shifts, horizontal shifts, and reflections) of power functions. Find the zeros and multiplicities of a polynomial function and use them to Find the zeros and multiplicities of a polynomial function and use them to determine whether the graph crosses or touches at each x-intercept. Remember that zeros are the x-coordinates of the x-intercepts. Find the y- intercept. Be able to state the power function that f resembles for large values of x and state the maximum number of turning points. Determine the behavior of the graph near the x-intercepts. Graph the function.
5 Review Problem Section 5.1 Fall 2006 Final Exam Determine the maximum number of turning points on the graph of f(x). Determine the behavior of the graph of fnear each x- intercept.
6 Objectives Section 5.2 Section 5.2 Find the domain of a rational function. Find vertical and horizontal or oblique asymptotes
7 Review Problem Section 5.2 Fall 2007 Final Exam
8 Finding Asymptotes pg 351
9 Review Problem Section 5.2 Fall 2007 Final Exam
10 Objectives Section 5.3 Section 5.3 Graph a rational function by analyzing the function: Find the domain, any asymptotes, any intercepts, and sketch the graph. Given the graph of a rational function, find the domain and range, any intercepts, and any asymptotes. Use your graphing calculator to find the approximate maximum value of a function in an applied (word) problem.
11 Review Problem Section 5.3 Fall 2006 Final Exam
12 Section 5.4 Solve rational and polynomial inequalities. Objectives Section 5.4
13 Review Problem Section 5.4 Fall 2007 Final Exam
14 Review Problem Section 5.4 Fall 2009 Final Exam
15 Objectives Section R.6 Section R.6 Use synthetic division to find the quotient and remainder. Use synthetic division to determine whether x-c is a factor of f(x).
16 Review Problem Section R.6/Ch 6 Fall 2008 Final Exam
17 Objectives Section 5.5 Section 5.5 Use the Factor Theorem to determine whether x-c is a factor of f(x). Know the maximum number of zeros a polynomial may have. List the potential rational zeros of a polynomial function. (Use the Rational Zeros Theorem.) Use the above information to find the real zeros of a polynomial function and write the function in factored form. Solve polynomial equations in the real number system by using the above information.
18 Review Problem Section 5.5 Fall 2006 Final Exam
19 Objectives Section 5.6 Section 5.6 Given the degree and some zeros of a polynomial with real coefficients, find the remaining complex zeros. Form a polynomial f(x) having given degree and complex zeros. Find the complex zeros of a polynomial function and write the function in factored form.
20 Review Problem Section 5.6 Fall 2006 Final Exam
21 Review Problem Section 5.6 Fall 2008 Final Exam
22 Objectives Section 6.1 Section 6.1 Find the composite of two functions at a given value of x. Find the composite of two functions and the domain of the composite function.
23 Review Problem Section 6.1 Fall 2007 Final Exam
24 Objectives Section 6.2 Section 6.2 Determine whether a function is one-to-one. Determine if two functions f and g are inverses of each other. Find the inverse of a function and state the domain and range of both and f 1 ( x). f ( x)
25 Review Problem Section 6.2 Fall 2007 Final Exam
26 Review Problem Section 6.2 Fall 2008 Final Exam
27 Objectives Section 6.3 Section 6.3 Graph without using a calculator in this section! x x Graph an exponential function f ( x) = a and transformations of f ( x) = a. State the domain, range, and horizontal asymptote. u v Solve exponential equations by using: If a = a then u = v.
28 Review Problem Section 6.3 Fall 2007 Final Exam
29 Review Problem Section 6.3 Fall 2005 Final Exam
30 Objectives Section 6.4 Section 6.4 Graph without using a calculator in this section! Change between exponential and logarithmic form of an equation. Find the exact value of a logarithm. Find the domain of a logarithmic function. Graph y = log a x, y = ln( x), and transformations of each. State the domain, range, and vertical asymptote. Solve logarithmic equations by changing to exponential form.
31 Review Problem Section 6.4 Fall 2007 Final Exam
32 Objectives Section 6.5 Section 6.5 Write an expression as a sum and/or difference of logarithms. Express powers as factors. Write an expression as a single logarithm.
33 Review Problem Section 6.5 Fall 2006 Final Exam
34 Section 6.6 Solve logarithmic and exponential equations. Be able to give the exact solution. Remember to check that solutions to logarithmic equations are in the domain. Objectives Section 6.6
35 Review Problem Section 6.6 Fall 2007 Final Exam
36 Section 6.7 Solve application problems involving compound interest. You will need a calculator. Objectives Section 6.7
37 Review Problem Section 6.7 Fall 2007 Final Exam
38 Review Problem Section 6.7 Fall 2008 Final Exam
39 Section 6.8 Solve application problems involving exponential growth and decay. Know how to find or use half-life of a substance in solving problems. You will need a calculator. Objectives Section 6.8
40 Review Problem Section 6.8 Final Exam Fall 2007
41 Review Problem Section 6.8 Final Exam Fall 2006
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Introduction. A rational function is a quotient of polynomial functions. It can be written in the form
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