2. PROPERTIES OF FUNCTIONS 111

injection. It is not a surjection because the range is not equal to the codomain. For example, there is no number in the domain with image 1 which is an element of the codomain. It is not an injection since more than one distinct element in the domain is mapped to the same element in the codomain. For example, f( 1) = f(1) but 1 6= 1 . Exercise ...

  Injection

PART 2 MODULE 1 LOGIC: STATEMENTS, NEGATIONS, …

PART 2 MODULE 1 LOGIC: STATEMENTS, NEGATIONS, QUANTIFIERS, TRUTH TABLES STATEMENTS A statement is a declarative sentence having truth value. Examples of statements:

PART 3 MODULE 2 MEASURES OF CENTRAL TENDENCY …

PART 3 MODULE 2 MEASURES OF CENTRAL TENDENCY EXAMPLE 3.2.1 To paraphrase Benjamin Disraeli: "There are lies, darn lies, and DAM STATISTICS." Compute the mean, median and mode for the following DAM STATISTICS:

  Measure, Example, Central, Module, Tendency, Module 2 measures of central tendency, Module 2 measures of central tendency example

Quiz #10 (Form A) KEY ANSWERS ARE IN BOLD ITALICS. b) 34

7) A fractal is an object a) that reveals new features at smaller scales b) that is symmetric c) that has proportional features d) whose length to width ratio is the golden mean 8) Which of the following is NOT an example of fractals? a) the number of spirals on a pineapple b) coastlines c) ferns d) coral 9) Fractal geometry has applications in

  Geometry, Fractal, Fractal geometry

Fourier Transform Examples - Florida State University

2 Formula Justi cations Equations (1), (3) and (5) readly say the same thing, (3) being the usual de nition. (Warning, not all textbooks de ne the these transforms the same way.)

  Example, Transform, Fourier, Fourier transform examples

CHAPTER 2

p;q;r;s;:::, and connectives or logical operators. A logical operator is either a unary operator, meaning it is applied to only a single proposition; or a binary operator, meaning it is applied to two propositions. Truth tables are used to exhibit the rela-tionship between the truth values of a compound proposition and the truth values of

  Chapter, Chapter 2, Connective

PART 1 MODULE 2 SET OPERATIONS, VENN DIAGRAMS SET …

B= {Casablanca, The Godfather Part 2, The Wizard of Oz, Citizen Kane, To Kill A Mockingbird} Set C below contains the five most passionate films according to the American Film Institute. C = {Gone With the Wind, Casablanca, West Side Story, An Affair To Remember, Roman Holiday}. Notice that some films appear on more than one of these lists.

  Wizards, Wizard of oz

PART 1 MODULE 3 VENN DIAGRAMS AND SURVEY …

A number of classicists were asked to identify their favorite epic poets. The results are summarized below. 62 appreciate Homer 40 appreciate Virgil 5 appreciate Gomer 2 appreciate Homer and Virgil and Gomer 3 appreciate Virgil and Gomer 20 appreciate Homer and Virgil 42 appreciate Homer and neither of the other two

  Otep

Indeterminate Forms - Florida State University

1 x) x= e.This is of the indeterminate form 1∞. We write exp(x) for exso to reduce the amount exponents. lim x→∞ (1 + 1 x)x= exp(ln( lim x→∞ (1 + 1 x)x)) = exp( lim x→∞ ln((1 + 1 x)x)) = exp( lim x→∞ xln(1 + 1 x)) = exp( lim x→∞ ln(1 + 1 x) 1/x) We can now apply L’Hopital’s since the limit is of the form 0 0. = exp ...

Trig Substitution - Florida State University

(a)completing the square; (b) u-substitution; (c)algebraic cleverness; (d)some combination of the above. P2.Once you’ve done this, make the appropriate substitution of xand dx. Make sure to use the simpli cations (i.e., the \square root removals") that result from the trig substitution! P3.Simplify the integrand as needed and integrate.

  Square, Completing, Completing the square, The square

Notes Combining Like Terms - Mayfield City School District

Example 1: 14m – 3n2 2– 2n + 3m 2 Example 1: 5x + 4x – 6 + 5x Note: all of your answers should be arranged so that the variables are in _____ order first, then in order from greatest to least _____. Watch out for the following common mistakes! Circle the mistakes below: Mistake #1: a2 – 4a + 5a 2a2

  Terms, Example, Like, Combining, Combining like terms, Example 2

Communication

2. Do ONE of the following: c a. Think of a creative way to describe yourself using, for example, a collage, short story or autobiography, drawing or series of photographs, or a song or skit. Using the aid you created, make a presentation to your counselor about yourself. c b. Choose a concept, product, or service in which you have great ...

  Communication, Example

TRANSITIONAL WORDS AND PHRASESrevised815

2. If you’re having company for dinner, try to get as much done in advance as possible. _____, set the table the day before. a. For instance b. In contrast c. Similarly The transition word indicates: illustration/example comparison contrast 3. _____ I’m very allergic to flowers, my boyfriend bought a bouquet of roses. a. Until b. Because

  Example