1st Grading

• Relation is a set of ordered pairs that are arranged in orderly manner
• Function is a relation in which each element of the domain corresponds to exactly one element of the range
• Not function

  A) X

  
• Piecewise Function is a function that is defined by two or more equations where each equations applies to a certain interval over a specified domain
• Piecewise function problem:

  A) d-1/0.5

  
• Operations on Functions:

  A) q(x) + f(x)

  
• Composition of Functions:

  A) composite

  
• Word Problem:

  A) f = k/L

  
• constant 2 - still a polynomial
• Rational expression - ratio of 2 polynomials
• ratio - comparison of two numbers
• extraneous solution is an apparent solution that does not solve its equation
• Word Problem #2:

  A) 12+x/25+x

  
• values - output of a function
• Functions - relationships between two variables
• Functions Notes:

  A) function

  B) x

  C) y

  D) mapped

  E) f such that

  F) set of all ordered pairs

  G) candidate

  H) equations

  
• Ways of writing ordered pairs:

  1. Graphing
  2. Table of Values
  3. Mapping
  4. Equations
  5. Sets
• Evaluation - process of finding output, by substituting the given values of variable and simplify
• 4 types of relations of ordered pairs:

  1. One to One Correspondence - each x is unique
  2. Many to One Correspondence - each x is unique to one y
  3. One to Many Correspondence - one x to y is unique
  4. Many to Many Correspondence - each x is unique to one y & one x to each y is unique
• Vertical line test - to determine if a graph represents a function, only one point intersection
• Domain and Range:

  A) Domain

  B) Range

  C) Linear Function

  D) Quadratic Function

  E) Polynomial Function

  F) Rational Function

  G) Square Root

  
• Domain and Range - If writing the set, dont repeat the values and arrange based on number line ex: -3, -1, 0, 3, 4
• [2.75] = 2 because it is greates integer
• Find Domain and Range #1:

  A) -2

  B) 1

  
• Find Domain and Range #2:

  A) 3

  B) 1

  C) 1