G11 GenMath 1st Q

• Functions a set of ordered pairs (x , y) such that no two ordered pairs have the same x- values but different y- values.
• Types of Function (Based on Degree)

  1. Constant function - Polynomial function of degree of zero.
  2. Linear function - Degree of one
  3. Quadratic function - Degree of two
  4. Cubic function - degree of three.
• The Vertical Line Test can be used to determine whether a graph represents a function.
• Each element of the range is paired with exactly one element of the domain is called One to One Function.

  
• If one element in the domain have more than one element in the range, this diagram is called One to Many Function.

  One to Many relations are not functions.

  
• Evaluating functions means replacing the variable in the function. In this case x, with a value from the functions domain and computing for the result. To denote that we are evaluating f at a for some a in the domain of f we write f(a).
• What type of Operation on Functions is this?

  Addition (𝒇 + 𝒈)(𝒙) = (𝒇 𝒙 + 𝒈)(𝒙)
• What type of Operation on Functions is this?

  Subtraction (𝒇 − 𝒈)(𝒙) = 𝒇 (𝒙) − 𝒈(𝒙)
• What type of Operation on Functions is this?

  Multiplication (𝒇 ∙ 𝒈)(𝒙) = 𝒇 (𝒙) ∙ 𝒈(𝒙)
• What type of Operation on Functions is this?

  Divison

  
• What type of Operation on Functions is this?

  Composition

  
• Rational Functions - Is a function that can be written in the form of:

  
• Restriction in Polynomial Function

  An algebraic expression is a polynomial if its satisfies the following conditions:

  • No variables should appear with negative exponent in the denominator.
  • Variables should not have a fractional exponent.
  • Variable should not appear under radical sign.