GENMATH 1Q

• FUNCTION

  • Relation between two sets in which the elements in the domain corresponds to exactly one element of the range
• RELATION

  • set of ordered pairs. (x , y)
• TYPES OF FUNCTION

  1. one-to-one
  2. many-to-one
• MANY-TO-ONE

  • function that connects two or more elements of the domain set with a single domain set x, and are connected to a single set y.
• ONE-TO-ONE

  • function in which each input value is mapped to one unique output value.
  • no two input elements have the same output value.
• ONE-TO-MANY

  • One x -value corresponds to multiple y -values.
  • Not considered a function.
• • All functions are relations, but not all relations are functions.
• PIECEWISE FUNCTION

  • compound function.
  • Defined by multiple sub functions where eac applies to a certain interval of the main function’s domain.
• EVALUATING FUNCTION

  • replacing the variable in the function with a value from the function’s domain and computing for the result.
• RATIONAL

  • Containing quantities that are expressible as a ratio of whole numbers
• POLYNOMIALS

  • Algebraic expression consisting of variables and coefficients 
• RATIONAL EXPRESSION

  • Ratio between two polynomials
  • $p/q$
• RATIONAL EQUATION

  • Equation containing at least one fraction whose denominator are polynomial, $p(x)/f(x)$
  • Fraction can be on one or both sides of the equation
• RATIONAL INEQUALITY

  • Rational equation + inequality symbol
  • $p(x)/q(x)>0$ where > can be replaced by <, ≤, ≥ 
  • Inequality symbol, one variable
• ASYMPTOTE

  • A line that a curve approaches, as it heads towards infinity
• DOMAIN

  • Input values
  • X-values 
  • The set of all x that will make the function defined
• RANGE

  • f(x)
  • Y-coordinate
  • Output values
  • The set of all possible output values that the function can produce.
• VERTICAL ASYMPTOTE

  • x=a is a vertical asymptote of a rational function if the graph either increases or decreases without bound as x-values approach from  the right or left
  • Value of x that will make the function undefined
• HORIZONTAL ASYMPTOTE

  • Parallel to x-axis
  • y=b is a horizontal asymptote if f(x)  gets closer to as x increases and decreases without bound
• HORIZONTAL ASYMPTOTE

  • If n < m, then y  = 0
  • If n >  m, then there is no horizontal asymptote
  • If n = m, then y = $a/b$
• INTERCEPTS

  • Point where the graph of the rational function intersects the x-axis or y-axis
• Y-INTERCEPT

  • Function value when x=0
• X-INTERCEPT

  • value of x that makes the numerator equal to zero but not the denominator
• EXTRANEOUS SOLUTION / FALSE SOLUTION

  • Denominator: Zero, thus, undefined
• name the inequality

  • the set of all x such that x is less than or equal to 2