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Classify equations as relations, functions or one-to-one functions

This Page: Part I: Review of various equation types
Part II Practice quiz- classify relations as functions, 1-to-1 or neither
Related: Functions in math|Interative Relation|Evaluating Functions|Vertical Line Test | Composition of functions | One to One Function|inverse of a function |Quiz on Classifying relations
To classify an equation as a function will always depend whether or not the given equation can have more than 1 element in the domain for any given element in the range. Some giveways include
  • Vertical lines which always have the equation x = some number
    • Example x= 2 or x = 5
  • Any equation that has y² in it should be examined very, very carefully
    • Example 1 Horizontal parbolas
      (parabolas that open to the side) such as x = y² is a parabola that has two distinct y values for every x. Therefore, the elements in the domain correspond with more than one element in the range, thus violating the rule for functions in math. In fact any parabola that opens horizontally is not a function because it will never pass the vertical line test
    • Example 2: Circles
      The equation of a circle also has a y² . Remember that the standard form equation of a circle takes the general form of (x-h)² + (y - k)² = r².
    • By the same logic as the circle, all hyperbolas and ellipses are not functions
  • All other potential functions must be carefully examined to see if it is possible to match an element in the domain with two distinct elements in the range, thus making such an equation a regular relation.
Practice Problems

Part I Remembering The look and Feel of Various Equation Types

Practice Problem One
    What is the difference between the following equations?
  • y = x +1
  • y = 1 + x
  • y - x = 1
  • y - x - 1 = 0

    Answer   
Practice Problem three
Practice Problem four
Practice Problem five
Practice Problem six
    Is y = x² a relation or a function? If so, is it a one-to-one function?

        Answer   

Practice Problem Seven
Practice Problem Eight
This Page: Part I: Review of various equation types
Part II Practice quiz- classify relations as functions, 1-to-1 or neither
Related: Functions in math|Interative Relation|Evaluating Functions|Vertical Line Test | Composition of functions | One to One Function|inverse of a function |Quiz on Classifying relations

Part II Quiz and Practice: Classify Relations

Practice Problem One
Is y = 3x + 1 a function,a one-to-one function or just a relation?
    Answer   


Practice Problem Two
Is y -2x = 1 a function,a one-to-one function or just a relation?

    Answer   

Practice Problem three
Is y -2x = 1 a function,a one-to-one function or just a relation?

    Answer   

Practice Problem Four
Is X² + y² = 25 a function,a one-to-one function or just a relation?

    Answer   

Practice Problem Five
Is y = 5 a function,a one-to-one function or just a relation?

    Answer   

Practice Problem Six
Is Y = X² + 2X+ 25 a function,a one-to-one function or just a relation?

    Answer   


This Page: Part I: Review of various equation types
Part II Practice quiz- classify relations as functions, 1-to-1 or neither
Related: Functions in math|Interative Relation|Evaluating Functions|Vertical Line Test | Composition of functions | One to One Function|inverse of a function |Quiz on Classifying relations
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