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# Pre-calculus Review

This is a collection of various mediums for students to use to review and study for their Pre-calculus exam.

by

Tweet## Catherine Bartholf

on 11 January 2010#### Transcript of Pre-calculus Review

Pre-calculus Review Polynomial Functions Rational Functions Exponential and Log Functions Trigonometric Functions Triangles Combinations and Compositions Domain and Range Fundamentals of Functions Factoring Graphing Divison Box Division Long Division Synthetic Division x-intercepts, also known as roots, are the zeros of the function Rational Zeros Test Asymptotes Intercepts Horizontal Asymptotes Vertical Asymptotes x-intercepts y-intercepts Holes Graphing Exponential Functions Logarithms Sine Cosine Tangent Law of Sines Law of Cosines Types SAS SSS SSA AAS This is a graph of a Sine wave with no shift This is a praph of a Cosine wave with no shift This is a Tangent graph with no shift Graphs of table above Oblique/Slant Asymptotes These examples are the same problem solved two different ways There are various methods used to factor equations. By examining the problem, you can determine which is the best method to use. http://www.analyzemath.com/polynomial2/polynomial2.htm http://www.rkm.com.au/ANIMATIONS/animation-sine-wave.html Curious to see how sine and cosine originate?

Check out this website for an animation of a sinusoidal wave! Visit this site to explore an interactive tutorial with a Java Applet. Domain is the x values on a coordinate plane while the range is the y values of the coordinate plane. Combinations and compositions are created using two functions.

Combinations use addition, subtraction, multiplication and division.

Compositions use one function value and plug that value into the other function. The Rational Zero Test can be used to determine all of the possible zeros of a function. Box division is another way to perform division of polynomials. It does not matter to what degree the polynomial is. Set the expression in the denominator equal to zero then solve. This helps to determine the domain. Test your knowledge of finding domain with these problems and then check your answers. (No peeking!) http://www.purplemath.com/modules/logrules.htm Visit this website to learn about the basic rules of logs, expanding logarithmic functions, and simplifying logs. You can graph two log functions and see where their point of intersection is to see where the functions are equal. Cotangent Secant Cosecant This is cosecant without shift This is cotangent without shift This is secant without shift Look at the degree of the polynomials in the numerator and the denominator.

1. If the denominator power > numerator power, then the horizontal asymptote (HA) is y=0

2. If the denominator power = numerator power, then the HA is y= ratio of the leading coefficients

3. If the denominator power<numerator power, then there is NO HA.

*Remember: Since the HA is an end behavior asymptote, the graph can across the HA in the middle. Slant asymptotes occur when the degree of the numerator is one more than the degree of the denominator. Where the graph crosses the x-axis Where the graph crosses the y-axis Standard Form Triangle http://www.algebralab.org/studyaids/studyaid.aspx?file=Trigonometry_LawSines.xml This site provides more info on solving oblique triangles. ASA

Full transcriptCheck out this website for an animation of a sinusoidal wave! Visit this site to explore an interactive tutorial with a Java Applet. Domain is the x values on a coordinate plane while the range is the y values of the coordinate plane. Combinations and compositions are created using two functions.

Combinations use addition, subtraction, multiplication and division.

Compositions use one function value and plug that value into the other function. The Rational Zero Test can be used to determine all of the possible zeros of a function. Box division is another way to perform division of polynomials. It does not matter to what degree the polynomial is. Set the expression in the denominator equal to zero then solve. This helps to determine the domain. Test your knowledge of finding domain with these problems and then check your answers. (No peeking!) http://www.purplemath.com/modules/logrules.htm Visit this website to learn about the basic rules of logs, expanding logarithmic functions, and simplifying logs. You can graph two log functions and see where their point of intersection is to see where the functions are equal. Cotangent Secant Cosecant This is cosecant without shift This is cotangent without shift This is secant without shift Look at the degree of the polynomials in the numerator and the denominator.

1. If the denominator power > numerator power, then the horizontal asymptote (HA) is y=0

2. If the denominator power = numerator power, then the HA is y= ratio of the leading coefficients

3. If the denominator power<numerator power, then there is NO HA.

*Remember: Since the HA is an end behavior asymptote, the graph can across the HA in the middle. Slant asymptotes occur when the degree of the numerator is one more than the degree of the denominator. Where the graph crosses the x-axis Where the graph crosses the y-axis Standard Form Triangle http://www.algebralab.org/studyaids/studyaid.aspx?file=Trigonometry_LawSines.xml This site provides more info on solving oblique triangles. ASA