Gen. Math Q1 Lessons

• Domain


  The set of first coordinates in an ordered pair
• Range


  The set of second coordinates in an ordered pair
• Finding domain and range from ordered pairs

  1. Identify the set of x-values (domain)

  2. Identify the set of y-values (range)
• Relation


  A set of ordered pairs
• Function


  A relation in which each element of the domain corresponds to exactly one element of the range
• Ordered pair relations


  • Relation F (function)
  • Relation G (not a function)
  • Relation H (function)
• Identifying functions from ordered pairs

  Check if each x-value has only one corresponding y-value
• Mapping diagram relations


  • Diagram 1 (function)
  • Diagram 2 (not a function)
  • Diagram 3 (function)
• Vertical line test


  A graph represents a function if and only if each vertical line intersects the graph at most once
• Graphs of functions


  • Graph 1 (function)
  • Graph 2 (not a function)
  • Graph 3 (not a function)
• Equations representing functions


  • y = 2x + 1 (function)
  • x^2 + y^2 = 1 (function)
  • x^2 + y - 4 = 0 (function)
  • y = x^2 - 2x + 2 (function)
  • y = √(x + 1) (function)
  • y = 2x + 1 / (x - 1) (function)
  • x^2 + y^2 = 0 (not a function)
• Vertical line test


  A method to determine if a graph represents a function
• Vertical line test


  • Small alum points
  • Tata man one two three four five six
• A big civilian that is not a function
• Function


  A relationship where each input has exactly one output
• How to identify if a graph is a function or not

  1. Digitized Salus representation

  2. Use equation
• Equations to determine if they represent a function

  • y = 2x + 1
  • x^2 + y^2 = 1
  • x^2 + y - 4 = 0
  • y = x^2 - 2x + 2
  • y = √(x + 1)
  • y = 2x + 1 / (x - 1)
• Linear equation


  A function because the graph is a straight line
• Quadratic equation


  A function because the graph is an upward parabola
• Rational equation


  A function because the graph has no vertical asymptotes
• x^2 + y^2 = 1 is not a function
• How to determine if x^2 + y^2 = 1 is a function

  1. Solve for y in terms of x

  2. Use the square root method
• Functions can be represented using ordered pairs
• Functions pass the vertical line test
• Ways to check if a relationship is a function


  • Use ordered pairs
  • Use mapping diagram
  • Use vertical line test
  • Graph the equation
• Linear, quadratic, and rational equations are functions
• When analyzing markets, a range of assumptions are made about the rationality of economic agents involved in the transactions
• The Wealth of Nations was written

  1776
• Rational


  (in classical economic theory) economic agents are able to consider the outcome of their choices and recognise the net benefits of each one
• Rational agents will select the choice which presents the highest benefits
• Consumers act rationally by

  Maximising their utility
• Producers act rationally by


  Selling goods/services in a way that maximises their profits
• Workers act rationally by


  Balancing welfare at work with consideration of both pay and benefits
• Governments act rationally by


  Placing the interests of the people they serve first in order to maximise their welfare
• Rationality in classical economic theory is a flawed assumption as people usually don't act rationally
• Marginal utility


  The additional utility (satisfaction) gained from the consumption of an additional product
• If you add up marginal utility for each unit you get total utility