 Graphing Calculator Math Worksheets Scientific Calculator Chart Maker   Graphing Calc Interactive Scientific Calc      Graphing Calc Interactive Scientific Calc       Graphing Calc Interactive Scientific Calc         Graphing Calc Interactive Scientific Calc   # Classify equations as relations, functions or one-to-one functions

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

Practice Problem three Is y - 5x = 1, a relation or a function? If so, is it a one-to-one function?

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

Practice Problem five
Is x = y² a function, a one-to-one function or just a relation?

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

Practice Problem Seven
Practice Problem Eight

#### Part II Quiz and Practice: Classify Relations

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

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

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

Practice Problem Four
Is X² + y² = 25 a function , a 1 to 1 function or just a relation?