Sample. Sample. Sample. Sample (1,2) (-1,1) (3,-1) (-3,-5) Sample (1,2) (-1,1) (3,-1) (-3,-5) Sample. (x, y) Domain: {-3, -1, 1, 3} (1,2) (-1,1)

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1 (-1,1) (1,2) Algebra 2 HS Mathematics Unit: 02 Lesson: 01 (3,-1) (-3,-5) Range: {-5, 1, 2, -1} (-1,1) (-3,-5) (1,2) (3,-1) (-1,1) (-3,-5) (1,2) (3,-1) Domain: {-3, -1, 1, 3} (1,2) (-1,1) (3,-1) (-3,-5) (, ) 2012, TESCCC 04/04/13 page 1 of 10

2 Characteristics of (0,0) Quadrant: II Quadrant: I ( -, + ) ( +, + ) Quadrant: III Quadrant: IV ( -, - ) ( +, - ) Relations and Functions KEY 1. Cartesian coordinate plane On the graph provided: A) Label each ais. B) Label each quadrant. C) Indicate whether coordinates would be positive or negative in each quadrant. Calculator Check On a calculator, press GRAPH, then arrow left and right. Coordinates appear on the screen. Do the signs of and match our notes? 2. Vocabular Complete the table to describe the given terms. Term Representation on Coordinate Plane Verbal Description Origin Intersection of the = 0 and = 0

3 Ordered Pair lines Intersection of the and aes Point (0, 0) Representation of the and coordinates Point (, ) Algebra 2 HS Mathematics Unit: 02 Lesson: , TESCCC 04/04/13 page 3 of 10

4 Characteristics of Relations and Functions KEY Term Representation on Coordinate Plane Verbal Description Relation Set of ordered pairs represented b a set of points, graph, or an equation Domain Domain: { -3, -1, 1, 3} Set of all the -coordinates in a relation Independent variable Range Range: { -5, -1, 1, 2} Set of all the -coordinates in a relation Dependent variable Function Relation in which each element of the domain is paired with eactl one element of the range Set of points in which values onl occur once Graph where an vertical line will onl cross the graph once

5 Characteristics of Relations and Functions KEY Algebra 2 HS Mathematics Unit: 02 Lesson: 01 Term Representation on Coordinate Plane Verbal Description Discrete Individual points Points not connected Continuous Line or smooth curve Infinite number of points Increasing Both the -values and the -values increase Intervals in the graph when the function goes up from left to right Decreasing -values increase and -values decrease Intervals in the graph when the function goes down from left to right 2012, TESCCC 04/04/13 page 5 of 10

6 Characteristics of Relations and Functions KEY 3. Function notation Functional notation is a method used to represent the point (, ) as (, f()). Other letters besides f ma be used in order to identif multiple functions b different letters. If f() = 2 + 3, find f(4) and f(-1). f(4) = 2(4) + 3 f(-1) = 2(-1) + 3 f(4) = 11 So the ordered pair ( 4, 11 ) is included in the function f(). f(-1) = 1 So the ordered pair ( -1, 1 ) is included in the function f(). A) Given that h(3) g( ) = and h( ) = , evaluate the following. g( 3) g( a + 1) a 2 + 2a + 3 B) In function notation, (, f()), which smbols represent the domain and range? Domain is, range is f(). C) What are the benefits of using function notation? Answers will var. Can be used to distinguish functions b letter. Gives the domain value in the problem. 4. Label the aes, the origin, and the quadrants of the coordinate plane below, and then graph the points in the set. {(-2, 5), (3, 4), (-3, -5), (0, 4), (1, 0), (4, 5), (0, -2)} A) Identif the domain. { -3, -2, 0, 1, 3, 4} B) Identif the range. { -5, -2, 0, 4, 5} C) Is the relation a function? Eplain our reasoning. No, the -values repeat. D) Is it continuous or discrete? Eplain our reasoning. Discrete, points are distinct and not connected.

7 Characteristics of Relations and Functions KEY Algebra 2 HS Mathematics Unit: 02 Lesson: Provide information about the relations graphed below. a. b. Identif the domain. { R, 2 < 4} or { 2 < 4} Identif the range. R, 4 3 { } or { 4 3} Identif the domain. { 0} Identif the range. { 0} 2012, TESCCC 04/04/13 page 7 of 10

8 b. Is the relation also a function? Yes Is the relation also a function? Yes Is it continuous or Is it continuous or discrete? discrete? Continuous over the Continuous over the domain domain On what interval(s) is On what interval(s) is it increasing? it increasing? 2 < < 0, 2 < < 4 > 0 On what interval(s) is On what interval(s) is it decreasing? it decreasing? 0 < < 2 None

9 Characteristics of Relations and Functions KEY Algebra 2 HS Mathematics Unit: 02 Lesson: Provide information about the equations given below. a. = 2 1 Complete the table of values. b. = Complete the table of values ERROR Sketch the graph. Sketch the graph. Identif the domain and range. Identif the domain and range. { R} Domain: 0 { } { 1} Domain: 0 { } Range: Range: Is the relation also a function? Is the relation also a function? Yes Yes Is it continuous or discrete? Is it continuous or discrete? Continuous over the domain Continuous over the domain What parent function best represents the data? What parent function best represents the data? 2012, TESCCC 04/04/13 page 9 of 10

10 Absolute Value Parent Function Square Root Parent Function