Math 421-Relations and Functions Review

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1 Math 1-Relations and Functions Review Name: SCO: RF1 Interpret and explain the relationships among data, graphs and situations. A. Graph, with or without technolog, a set of data, and determine the restrictions on the domain and range. B. Explain wh data points should or should not be connected on the graph for a situation. C. Describe a possible situation for a given graph. D. Sketch a possible graph for a given situation. E. Determine, and express in a variet of was, the domain and range of a graph, a set of ordered pairs, or a table of values. Section(s) in Foundations and Pre-Calculus Mathematics 1 text that address the specific curriculum outcome with relevant Achievement Indicators in brackets:.1 (E),. (E),.3 (C D),. (A B E),. (B E) SCO: RF Demonstrate an understanding of relations and functions. [ A. Explain, using examples, wh some relations are not functions but all functions are relations. B. Determine if a set of ordered pairs represents a function. C. Sort a set of graphs as functions or non-functions. D. Generalize and explain rules for determining whether graphs and sets of ordered pairs represent functions. Section(s) in Foundations and Pre-Calculus Mathematics 1 text that address the specific curriculum outcome with relevant Achievement Indicators in brackets:. (A B D),. (D),. (C D) SCO: RF Describe and represent linear relations, using: words; ordered pairs; tables of values; graphs; equations. A. Identif independent and dependent variables in a given context. B. Determine whether a situation represents a linear relation, and explain wh or wh not. C. Determine whether a graph represents a linear relation, and explain wh or wh not. D. Determine whether a table of values or a set of ordered pairs represents a linear relation, and explain wh or wh not. E. Draw a graph from a set of ordered pairs within a given situation, and determine whether the relationship between the variables is linear. F. Determine whether an equation represents a linear relation, and explain wh or wh not. G. Match corresponding representations of linear relations. Section(s) in Foundations and Pre-Calculus Mathematics 1 text that address the specific curriculum outcome with relevant Achievement Indicators in brackets:. (A),. (A),. (A B C D E F G) SCO: RF Determine the characteristics of the graphs of linear relations, including the: intercepts; slope; domain; range. A. Determine the intercepts of the graph of a linear relation, and state the intercepts as values or ordered pairs. B. Determine the slope of the graph of a linear relation. C. Determine the domain and range of the graph of a linear relation. D. Sketch a linear relation that has one intercept, two intercepts or an infinite number of intercepts. E. Identif the graph that corresponds to a given slope and -intercept. F. Identif the slope and -intercept that correspond to a given graph. G. Solve a contextual problem that involves intercepts, slope, domain or range of a linear relation. Section(s) in Foundations and Pre-Calculus Mathematics 1 text that address the specific curriculum outcome with relevant Achievement Indicators in brackets:.7 (A C E G),.1 (B D),. (E F G) (NOTE:.1 and. are in the next unit) SCO: RF Represent a linear function using function notation. A. Express the equation of a linear function in two variables, using function notation. B. Express an equation given in function notation as a linear function in two variables. C. Determine the related range value, given a domain value, for a linear function; e.g., if f (x) = 3x, determine f ( 1). D. Determine the related domain value, given a range value, for a linear function; e.g., if g(t) = 7+t, determine t so that g(t) = 1. E. Sketch the graph of a linear function expressed in function notation. Section(s) in Foundations and Pre-Calculus Mathematics 1 text that address the specific curriculum outcome with relevant Achievement Indicators in brackets:. (A B C D),. (C D),.7 (E)

2 John Kell Martin Natalie Shoe Size Sample Problems: 1) Show each relation as a set of ordered pairs, table of values, arrow diagram, graph, write in words, and give the equation where applicable. Also, list the domain and range of each. Representation Relation 1: Shoe Sizes Relation : Numbers Set of Ordered Pairs {(,-), (3,-), (, -), (-, 1)} Table of Values Arrow Diagram Graph Shoe Sizes of Students In words Student Equation NOT APPLICABLE Domain Range

3 Distance from home (km) ) Convert between was of representing a relation as indicated. i) Here are some families and the number of das the spent camping last summer. ii) Consider the relation represented b this arrow diagram. Represent the relation as a set of ordered pairs. Gamble (1); Smith (); Clark (1); Richardson (1); Ferrish (1). Represent the relation as an arrow diagram is the number of people living in House R House P House Q House S iii) Capital cities can be associated with the province or territor the are in. Describe this relation in words. Capital Cit Victoria Edmonton Regina Winnipeg Whitehorse Yellowknife Iqaluit Province/Territor British Columbia Alberta Saskatchewan Manitoba Yukon Northwest Territories Nunavut a. The relation shows the association is the capital of from a set of capital cities to a set of provinces and territories. b. The relation shows the association is the largest cit of from a set of capital cities to a set of provinces and territories. c. The relation shows the association is the capital of from a set of provinces and territories to a set of capital cities. d. The relation shows the association is in the province/territor of from a set of provinces and territories to a set of capital cities. 3. Joshua went on a bike ride. For part of the ride, Joshua stopped to pla in a park with a friend. Which segment of the graph best describes this part of his bike ride? Joshua's Bike Ride 3 A B C a. CD b. AB c. OA d. BC 1 O 1 1 Time (min) D

4 Distance from home (km). A student drew a graph to represent this situation. Lenora starts her 3.-km walk home from school. After walking 1 km in min, she stops to talk to a friend. She talks for 1 min and then continues walking at the same pace. Fifteen minutes later, she stops for min to rest. She starts walking at the same pace again and after 1 min, she decides to jog the rest of the wa home. 3. Lenora's Walk Home Describe an errors in the student s graph Time (min). Determine if the following relations are functions. (-3, -), (-1, -), (-, ), (, 7) (, ), (3, 7), (9, ), (, 1) has a height of 1 cm 173 cm 1 cm 1 cm Sharon Petra Ammon Daniel Andrew x

5 Mass (kg). For the function, determine 7. For the function, determine x when.. The equation represents the total cost, C dollars, for a wedding banquet when p people attend. a) Write the function in function notation. b) Determine C(1) and explain what this number represents. c) Determine the value of p when C(p) = 9 and explain what this number represents. 9. Determine the domain and range for the following. (,), (,), (3,), (-7, ) has a shoe size of John Kell Martin Natalie 9 1 m Ages and Masses of People = f(x) x 1 1 a Age (ears) x x f(x) = x

6 Speed (m/s) 1. This is a graph of the function. Determine the range value when the domain value is 3. g(x) = x + 3 x 11. This graph shows the speed of a hot air balloon, s, as a function of time, t. s 1 1 Speed of a Hot Air Balloon a. Identif the independent and dependent variables. Independent = Dependent = b. When does the hot air balloon reach a speed of 1 m/s? c. What is the maximum speed reached? 1 t Time (s) d. Explain wh the points on the graph are connected? 1. Which table of values represents a linear relation? i) Distance (m) 1 1 Time (s) 1 3 ii) iii) Time (s) Distance (m) 1 3 Time (s) 1 3 Speed (m/s) Which equations represent linear relations? Create tables of values if necessar. a) b) c)

7 Volume (L) 1. This graph represents a 1-L hot-water tank being filled at a constant rate. Determine the rate of change of the relation V Filling a Hot-Water Tank (, 7) (, 1) 1 3 t Time (min) 1. This set of ordered pairs represents a linear relation. Determine its rate of change. 1. Which graphs have: i) a negative rate of change? ii) a positive rate of change? iii) neither a negative nor a positive rate of change? a) b) c) x x x 17. Sketch a graph of the linear function.

8 Distance (m) Distance (m) Distance (m) Distance (m) Distance (km) 1. This graph shows distance, d kilometres, as a function of time, t minutes. Determine the vertical and horizontal intercepts. 1 d d = f(t) Vertical intercept = Horizontal intercept = 1 1 t Time (min) 19. Each graph below shows distance, d metres, as a function of time, t hours. Circle the graph which has a rate of change of.7 m/h and a vertical intercept of 3 m. 1 d 1 d d = h(t) d = f(t) t Time (h) t Time (h) 1 d 1 d d = g(t) d = k(t) t Time (h) t Time (h)

Math 10 - Unit 6 - Functions - UNIT REVIEW WORKSHEET

Class: Date: Math 10 - Unit 6 - Functions - UNIT REVIEW WORKSHEET Multiple Choice Identify the choice that best answers the question. 1. Which set of ordered pairs does not represent a function? Ï i) Ì