<p> MATH 12 PRINCIPLES A1 NOTES: REVIEW RELATIONS, FUNCTIONS, DOMAIN AND RANGE, AND FUNCTION NOTATION</p><p>A. RELATION: A set of ordered pairs in which one value depends on the other value.</p><p>A relation can be represented in several ways: 1) as a set of ordered pairs 2) As a table of values</p><p>3) as a graph 4) as an equation </p><p></p><p>   </p><p></p><p></p><p>B. DOMAIN AND RANGE 1. Domain: the set of first (independent) 2. Range: the set of second (dependent) values for which a relation is defined. values for which a relation is defined.</p><p>Examples:</p><p>Relation Domain Range 1,5,3,6 x -5 -5 2 y 3 1 0</p><p></p><p> </p><p></p><p> 1 Relation Domain Range y  x 2 y  x 1 y  x y  x 2  3 y  x  3 1 y  1 x  2</p><p>B. FUNCTION: A relation in which there is only one second value for each first value.</p><p>Function Example Non-Function Example</p><p>Equation: y  x 2 Equation: x  y 2</p><p>Ordered Pairs: Ordered Pairs:</p><p> x -3 -2 -1 0 1 2 3 x y y -3 -2 -1 0 1 2 3</p><p>Equation Test (Ordered Pair Test) for a Function: If a value of ___ can be found which produces more than ___ value of ____ in the equation, then the equation ______represent a ______. If there are no values of x which produce more than ____ value of ____, then the equation does represent an ______.</p><p></p><p>  </p><p>Graphing Test (Vertical Line Test) for a Function: If no two points on the graph of a relation can be joined with a vertical line, then the graph represents a function.</p><p>2 C. FUNCTION NOTATION i) for Equations Eg 1) if f (x)  3x 2  2x  5 , evaluate: a) f (2) b) f (2)</p><p> c) f (x 1) (in simplest form) d) 2 f (x) 1 (in simplest form)</p><p> e) Find a such that f (a)  0 </p><p>Eg 2) If f (x)  3x  2 and g(x)  x 2 , determine: a) f (g(x)) b) g( f (x))</p><p> c) f ( f (x)) d) g(g(x))</p><p> ii) for Graphs</p><p>3 </p><p></p><p>   </p><p></p><p> The function y  f (x) is graphed above. 1) Determine: 2) Solve for x: a) f (0) b) f (8) a) f (x)  0</p><p> b) f (x)  1</p><p>Homework: A1 worksheet #(1,2)ace,4a,8bdfhil,10bce,11a-d,fh,12be,13cd,14all,15a- d,16a-f</p><p>4</p>