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