Presentation Transcript
Relation :Relation The pairing of elements of one set with the elements of another set. A relation is often written as: Abscissa The first element of an ordered pair.
The set of abscissa in a relation is called the Domain. Ordinate The second element of an ordered pair.
The set of ordinates in a relation is called the Range.
Example 1 :Example 1
Ordered Pairs :Ordered Pairs Ordered pairs can be represented in a variety of ways:
A table A pictorial representation Rule or Equation
(Graph) (Some, but not All)
Example 3 :Example 3 The domain appears to include:
The range appears to include: The domain appears to include:
The range appears to include: All real numbers (ℝ) All real numbers (ℝ) All real numbers (ℝ) All non-negative real numbers (ℝ)
Slide 6:Forward I'm heavy,
backwards I'm not.
What am I?
Function :Function A relation in which each element of the domain is paired with exactly one element in the range. D = { }
R = { }
Function? Why or Why not? D = { }
R = { }
Function? Why or Why not? A set of ordered pairs in which no two pairs have the same first element.
Vertical Line Test :Vertical Line Test If every vertical line drawn on the graph of a relation passes through no more than one point of the graph, then the relation is a function. No matter where the vertical line is moved, it only passes through one point. There are several places in which the vertical line passes through the function more than once.
Example 5 :Example 5 Because of the shading, a vertical line at x = 1, passes through infinitely many points. No matter where a vertical line is placed, it passes through the graph exactly once.
Function Notation :Function Notation The mathematical symbols indicating that an expression is a function. Every function can be evaluated for each value in its domain. Read as the function evaluated at -4 is equal to -296. Read as the function evaluated at 9 is equal to 23. The ordered pair (x, y) can be written in the form (x, f(x)).
Example 7 :Example 7
Example 8 :Example 8 Any value that makes the denominator equal to zero must be excluded from the domain The domain is all real numbers except 0 and 4. Any value that makes the radicand negative must be excluded from the domain, since the square root of a negative numbers is not a real number
HW: Page 9 (5 – 53 evens) :HW: Page 9 (5 – 53 evens)