Mathematics. Session. Functions, Limits and Continuity-1. Session Objectives. Function Domain and Range Some Standard Real Functions Algebra of Real Functions Even and Odd Functions Limit of a Function; Left Hand and Right Hand Limit

ByPRECALCULUS I. Functions and Graphs Function, domain, independent variable Graph, increasing/decreasing, even/odd. Dr. Claude S. Moore Danville Community College. Definition: Function.

BySection 2.3. Differentiation Formulas. DIFFERENTIATION FORMULAS FOR BASIC FUNCTIONS. 1. The derivative of a constant function, f ( x ) = c. 2. The derivative of the identity function, f ( x ) = x. THE POWER RULE.

ByReal-Valued Functions of a Real Variable and Their Graphs. Lecture 43 Section 9.1 Wed, Apr 18, 2007. Functions. We will consider real-valued functions that are of interest in studying the efficiency of algorithms. Power functions Logarithmic functions Exponential functions.

By3.3 Library of Functions, Piecewise-Defined Functions. A linear function is a function of the form. f(x)=mx+b. The graph of a linear function is a line with a slope m and y- intercept b. (0,b). A constant function is a function of the form. f(x)=b. y. b. x.

ByBasic Differentiation Rules. Lesson 3.2A. Basic Derivatives. Constant function Given f(x) = k Then f’(x) = 0 Power Function Given f(x) = x n Then . Try It Out. Use combinations of the two techniques to take derivatives of the following. Basic Rules. Constant multiple Sum Rule

By1-3 Graphing Linear Equations. Pre Calc A. Vocabulary. X-intercept Y-intercept Slope Slope intercept form Standard form Zeros of the function Constant function. Ex 17:. Graph x + 2y – 4 = 0 using the x- and y-intercepts. y = -.5x + 4. 3x + y = 6.

BySection 3.4. Objectives: Find function values Use the vertical line test Define increasing, decreasing and constant functions Interpret Domain and Range of a function Graphically and Algebraically. * f(w) * f(x) * f(z) * f(5) * 3 * 4 * - 9. x * z *

ByBoolean Algebra. Boolean Algebra. A Boolean algebra A set of operators (e.g. the binary operators: +, •, INV) A set of axioms or postulates. Postulates. Commutative x+y = y+x x •y=y•x Distributive x+(y•z)=(x+y)•(x+z) x•(y+z)=x•y+x•z Identities x+0=x x•1=x

By10.3: Continuity. Definition of Continuity . A function f is continuous at a point x = c if 1. 2. f ( c ) exists 3. A function f is continuous on the open interval ( a , b ) if it is continuous at each point on the interval.

ByDiscrete Random Variables. : 9 10 11 12. Numerical Outcomes. Consider associating a numerical value with each sample point in a sample space. (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

By1.6 part I Parent Functions. You should be familiar with the shapes of these basic functions. . Library of Functions. 1.6 Parent Functions. • The constant function, f(x) = c • The linear function, f(x) = x • The absolute value function, f(x) = |x|

ByThe Limit Theorems. Limit of a Constant Function. If f(x)=k , where k is a constant, then Example: f(x)=4 Find the limit as x approaches 3. Limit of the Identity Function. If f(x)=x, then Example: f(x)=x Find the limit as x approaches 3. Limit of a Constant Times a Function.

ByLesson 1.2. Functions and Their Graphs. Lance Barber, Benjamin Brayton, and Abel Bastarache. Constant Function. This function occurs when “y” equals a constant, or, more simply put, y=k. Identity Function. This function possesses both a range and a domain, making it y=x. Quadratic Equation.

Byof FUNCTION TRANSFORMATIONS. Functional Metaphors. Constant. A constant function is like a table because it stays nice and level. Linear. A linear function is like a hill. If the slope is positive you are climbing up. If the slope is negative you can be skiing down. . Quadratic.

ByChapter 3 Section 4: Library of Functions. In this section, we will… Graph the Library of Functions (a.k.a. Basic Functions) Graph Piecewise Defined Functions. Constant Function. Linear Function. These graphs should: be straight (use a straight-edge) extend the length of the graph

ByFunctions. Definition and notation. Definition: A function f from a set X to a set Y is a relationship between elements of X and Y with the property that each element of X is related to a unique element of Y. Denoted f:X →Y .

ByPre- Calculus 1. Do Now. Today’s Agenda. Today’s Objectives :. SWBAT… Sketch graphs of parent functions Define domains and ranges of common parent functions Graph functions on a calculator with a restricted domain Graph absolute value functions

ByDerivatives. By: Jenn Gulya. The derivative of a function f with respect to the variable is the function f ‘ whose value at x, if the limit exists, is:. This value is, also, representative of the slope of the function at a point. When f'(a) doesn't exist.

ByGeneral rules: Find big-O. f (n) = k = O(1) f ( n ) = a k n k + a k-1 n k-1 + . . . + a 1 n 1 + a 0 = O( n k ) Other functions, try to find the dominant term according to the growth rate of the well known functions Example f(n)=5n 2 +2 n f(n)=5n 2 +3nlog(n).

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