Pre-Calc: 1.1 Relations & Functions

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)