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### PP1 Presentation

1. 1. Chapter 1<br />Section 1.1<br />Functions and their Representation<br />
2. 2. Domain and Range<br />Domain<br />The set A or X values of an equation of function<br />Range<br />The set of B or Y values of an equation<br />Also known as output values<br />These numbers include:<br />Individual numbers<br />All real numbers<br />Can include +/- Infinity<br />Can also exclude zero<br />
3. 3. Functions and their Representation<br />This graph passes the vertical line test.<br />Functions<br />Each element (input) matches and is set to exactly one and only one output. (A to B)<br />Testing a function<br />Vertical line test<br />Method used for determining if a graph is or is not a function<br />Wikipedia. 2010.<br />Functions. <br />
4. 4. Vertical Line Test<br />What exactly does it do?<br />Tests that there is only one Y output for an X input.<br />Is a function<br />Not a function<br />UNCW EDU<br />T. Barron & S. Kastberg.<br />University of Georgia<br />
5. 5. Inverse Functions<br />Exception to the vertical line test?<br />Inverse Functions<br />Function are A to B (X,Y)<br />Inverse functions are B to A (Y,X)<br />Ex. To left is function along with it’s inverse.<br />Think Quest. 2010.<br />Inverse Functions.<br />
6. 6. Inverse Functions<br />Horizontal Line Test<br />Used in cases of inverse functions<br />Determines if the graph is a function or not<br />Below is example of a plot and its inverse<br />
7. 7. Representations of Functions<br />Four possible ways to represent a function<br />Verbally<br />Description in words<br />Visually<br />By a graph<br />Numerically<br />Table of values<br />Algebraically<br />Explicit formula<br />
8. 8. Increasing Functions<br />The Y-value increases as the X-value increases<br />f(x1) < f(x2) whenever; x1 < x2<br />Increasing sections of a graph<br />Math Is Fun. 2010.<br />Increasing Functions<br />
9. 9. Decreasing Functions<br />The Y-value decreases as the X-value increases<br />f(x1) > f(x2) whenever; x1 < x2<br />Decreasing section of a graph<br />Math Is Fun. 2010.<br />Decreasing Functions<br />
10. 10. Chapter 1<br />Section 1.2<br />Catalog of Essential Functions<br />
11. 11. Mathematical Modeling<br />What is mathematical modeling?<br />Mathematical representation (often by means of a function or an equation) of real-world phenomenon<br />Types of Models<br />Linear<br />y=f(x)=mx+b<br />Polynomials<br />P(x)= x2 − 4x + 7<br />Cubic Functions<br />C(x)=ax3 + bx2 + cx + d<br />
12. 12. Linear Equations<br />Graph of the function is a line<br />y=mx+b<br />y is the range<br />m is the slope<br />b is the y-intercept<br />Wikipedia.org. 2010.<br />Linear Functions.<br />
13. 13. Polynomial Functions<br />Graph of the function depends on the degree<br />Degree<br />The power of the coefficient and its variable<br />P(x)= x2 − 4x + 7<br />Degree of the above equation is 2.<br />Example to left is polynomial of degree 2<br />Wikipedia.org. 2010.<br />Polynomial Functions<br />
14. 14. Cubic Functions<br />A polynomial of a degree 3<br />C(x)=ax3 + bx2 + cx + d<br />Wikipedia.org. 2010.<br />Cubic Functions.<br />
15. 15. Other Type of Functions<br />Rational Functions<br />Wikipedia.org. 2010.<br />Trigonometric Functions<br />f(x)=sin x<br />f(x)=cos x<br />f(x)=tan x<br />To right is example of f(x)=sin x<br />Analyze Math. 2007.<br />Sin x Function<br />
16. 16. Other References<br />Wikipedia. http://www.wikipedia.org/<br />Google Images. http://www.google.com/<br />Essential Calculus: Early Transcendentals. James Stewart. pp(1-18). 2007.<br />