Part 2 Relations & Functions (II)

I. Vocabulary: relation: a collection of ordered pairs relating elements of one set (domain) to elements of another (range) function: a relation such that each element of the domain relates to only one element of the range continuous: describes a function of which the graph is a smooth, unbroken curve II. Determine if a Relation is a Function: This section presents five methods to determine if a relation is a function: Ordered pairs: f(x) = {(1, 2), (0, 3), (-5, 3)} YES Table of values: x f(x) -2 5 4 4 0 3 -1 2 YES Mapping: A diagram with arrows connecting elements from one set to another. YES Graph: A graph with a vertical line test. YES Graph: A graph of a function. YES III. Evaluate the Function Notation: Given f(x) = 3x^2 - 5x f(0) = 0 f(3) = 42 f(-2) = 22 f(a+h) = 3a^2 + 6ah + 3h^2 + 5a + 5h IV. FIND THE DOMAIN AND RANGE OF A FUNCTION: domain - x-values range - y-values f(x) = {(-1, 2), (0, 4), (4, -2), (5, -1), (7, 8)} domain: -1, 0, 4, 5, 7 range: 1, 2, 4, 8 V. DOMAIN AND RANGE WRITTEN IN INTERVAL NOTATION: if the domain is from 0 < x < 7: (0, 7) if the domain is from 0 <= x <= 7: [0, 7] if the domain is from 0^2 x^5 7: (0, 7) if the domain is from 0 to 3: (-0, 3) if the domain is from 5 to infinity: (5, infinity) if the domain is from negative infinity to infinity: [(-infinity, infinity)] open circle on a graph means: open interval () closed circle on a graph means: closed interval [] if a point is ON a graph: closed interval [] graph domain: (4, 5) range: (1, 3) graph domain: (-infinity, infinity) range: [6, infinity) list domain and range: * domain: [0, infinity) * range: (-infinity, 0] VI. INCREASING/DECREASING / CONSTANT/END BEHAVIOR / MAX/MIN: analyze the graph of a function below 3 2 5-4 2 -5 domain \((-\infty,\infty)\) range \(\frac{[-4,\infty\rangle}{u=2}\) rel. max [03 \(-5,2(moln~2),3\}\) yint: rel. min: \(\frac{\{-4,-1\}}{\{-45}\) xint abs. max: dne abs, min inc \(\{-\frac{1}{2},2\}=\{4,10\}\) dec(14) \[x\rightarrow\infty,\] con as \(x\rightarrow-\infty,\) y 2 ५ 2 -2 2 -2 -4 domain: (0) range [1] rel. min: 2 yint rel. max: (2) \[\frac{(-00,\infty)}{u=0}\] xint \([0,=\frac{7}{7}]\) inc dec:(1)(1) as \(x\rightarrow\infty,\) y con 1.13