Fair Game Review. Chapter 5. Input, x Output, y. 1. Input, x Output, y. Describe the pattern of inputs x and outputs y.

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1 Name Date Chapter Fair Game Review Describe the pattern of inputs and outputs.. Input, utput,. 8 Input, utput,. Input, 9. utput, 8 Input, utput, 9. The table shows the number of customers in hours. Describe the inputs and outputs. Hours, Customers, Copright Big Ideas Learning, LLC Big Ideas Math Algebra

2 Name Date Chapter Fair Game Review (continued) Draw a mapping diagram for the graph. Then describe the pattern of inputs and outputs In basketball, for each shot ou make from inside the three-point circle, ou score two points. Draw a mapping diagram for inputs,,,, and 8. Big Ideas Math Algebra Copright Big Ideas Learning, LLC

3 Name Date. Domain and Range of a Function For use with Activit. Essential Question How can ou find the domain and range of a function? ACTIVITY: The Domain and Range of a Function Work with a partner. In Activit in Section., ou completed the table shown below. The table shows the number of adult and child tickets sold for a school concert. input output Number of Adult Tickets, Number of Child Tickets, 8 The variables and are related b the linear equation + =. a. Write the equation in function form b solving for. b. The domain of a function is the set of all input values. Find the domain of the function represented b the table. Domain = Wh is = not in the domain of the function? Wh is = not in the domain of the function? c. The range of a function is the set of all output values. Find the range of the function represented b the table. Range = Copright Big Ideas Learning, LLC Big Ideas Math Algebra

4 Name Date. Domain and Range of a Function (continued) d. Functions can be described in man was. b an equation b an input-output table in words b a graph as a set of ordered pairs Use the graph to write the function as a set of ordered pairs ACTIVITY: Finding Domains and Ranges Work with a partner. Complete each input-output table. Find the domain and range of each function represented b the table. a. = + b. = c. d Big Ideas Math Algebra Copright Big Ideas Learning, LLC

5 Name Date. Domain and Range of a Function (continued) What Is Your Answer?. IN YUR WN WRDS How can ou find the domain and range of a function?. The following are general rules for finding a person s foot length. To find the length (in inches) of a woman s foot, divide her shoe size b and add 7. To find the length (in inches) of a man s foot, divide his shoe size b and add 7.. a. Write an equation for one of the statements. b. Make an input-output table for the function in part (a). Use shoe sizes to. c. Label the domain and range of the function represented b the table. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7

6 Name Date. Practice For use after Lesson. Find the domain and range of the function represented b the graph... Complete the input-output table for the function. Then find the domain and range of the function represented b the table.. =. = +. A factor that makes frozen pies produces pies per minute. a. Write an equation that represents the number of pies made each hour. b. Create an input-output table for the equation in part (a). Use inputs,,, 8, and. c. Find the domain and range of the function represented b the table. 8 Big Ideas Math Algebra Copright Big Ideas Learning, LLC

7 Name Date Etension. Practice For use after Etension. Determine whether the relation is a function.. (, 7 ), (, ), (, ), (, ), (, ). (,, ) (,, ) (,, ) (,, ) ( 9, 9). Input utput. 7 8 Input utput..... Input, utput,... Input, utput, Copright Big Ideas Learning, LLC Big Ideas Math Algebra 9

8 Name Date Etension. Practice (continued) Determine whether the graph represents a function Let represent the number of each month. (For eample, = for Januar.) Let represent the number of das in month. Do not consider a leap ear. a. Complete the table. Input, utput, b. Does the relation represent a function? Eplain. c. When ou switch the inputs and outputs of this relation, is the resulting relation a function? Big Ideas Math Algebra Copright Big Ideas Learning, LLC

9 Name Date Discrete and Continuous Domains. For use with Activit. Essential Question How can ou decide whether the domain of a function is discrete or continuous? EXAMPLE: Discrete and Continuous Domains In Activities and in Section., ou studied two real-life problems represented b the same equation. + = or = + 8 a. 9 = + 8 onl points on the graph 8 7 b Domain (-values):,,,, Range ( -values): 8,,,, The domain is discrete because it consists of onl the numbers,,,, and. = + 8 all points on line segment 8 7 Copright Big Ideas Learning, LLC Domain (-values): Range ( -values): 8 The domain is continuous because it consists of all numbers from and on the number line. Big Ideas Math Algebra

10 Name Date. Discrete and Continuous Domains (continued) ACTIVITY: Discrete and Continuous Domains Work with a partner. Write a function to represent each problem. Graph each function. Describe the domain and range of each function. Is the domain discrete or continuous? a. You are in charge of reserving hotel b. The airline ou are using for the soccer rooms for a outh soccer team. Each trip needs an estimate of the total weight room costs $9, plus $ ta, per of the team s luggage. You determine night. You need each room for two that there will be pieces of luggage nights. You need to rooms. and each piece will weigh from to Write a function for the total hotel pounds. Write a function for the cost. total weight of the luggage. Total hotel cost Hotel Reservations Number of rooms Total weight of luggage Luggage Weight 7 7 Pounds per piece Big Ideas Math Algebra Copright Big Ideas Learning, LLC

11 Name Date. Discrete and Continuous Domains (continued) What Is Your Answer?. IN YUR WN WRDS How can ou decide whether the domain of a function is discrete or continuous? Describe two real-life eamples of functions: one with a discrete domain and one with a continuous domain. Copright Big Ideas Learning, LLC Big Ideas Math Algebra

12 Name Date. Practice For use after Lesson. Graph the function. Is the domain discrete or continuous?. Input utput. Length, Area, (inches) (square inches) Input Shirts, utput Cost, (dollars) The function c = + m represents the amount of calories ou burn after m minutes of eercising. Graph the function using a domain of,,, and. Is the domain discrete or continuous?. You bu cards to send to famil and friends for their birthdas. The function =. represents the cost of the number of cards ou bu. a. Is 8 in the domain? Eplain. b. Is in the range? Eplain. Big Ideas Math Algebra Copright Big Ideas Learning, LLC

13 Name Date. Linear Function Patterns For use with Activit. Essential Question How can ou use a linear function to describe a linear pattern? ACTIVITY: Finding Linear Patterns Work with a partner. Plot the points from the table in a coordinate plane. Write a linear equation for the function. a. 8 b c. d. 8 8 Copright Big Ideas Learning, LLC Big Ideas Math Algebra

14 Name Date. Linear Function Patterns (continued) ACTIVITY: Finding Linear Patterns Work with a partner. The table shows a familiar linear pattern from geometr. Write a linear function that relates to. What do the variables and represent? Graph the linear function. a. b. π π π 8π π 8 Big Ideas Math Algebra Copright Big Ideas Learning, LLC

15 Name Date. Linear Function Patterns (continued) c. d What Is Your Answer?. IN YUR WN WRDS How can ou use a linear function to describe a linear pattern?. Describe the strateg ou used to find the linear functions in Activities and. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7

16 Name Date. Practice For use after Lesson. Use the graph or the table to write a linear function that relates to The table shows the distance traveled (in miles) after hours. a. Graph the data. Is the domain discrete or continuous? b. Write a linear function that relates to. c. What is the distance traveled after three hours? 8 Big Ideas Math Algebra Copright Big Ideas Learning, LLC

17 Name Date. Function Notation For use with Activit. Essential Question How can ou use function notation to represent a function? B naming a function f, ou can write the function using function notation. ( ) f = Function notation This is read as f of equals minus. The notation f () is another name for. When function notation is used, the parentheses do not impl multiplication. You can use letters other than f to name a function. The letters g, h, j, and k are often used to name functions. ACTIVITY: Matching Functions with Their Graphs Work with a partner. Match each function with its graph. a. f( ) = b. g ( ) = + c. h ( ) = d. f( ) = A. B. C. D. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 9

18 Name Date. Function Notation (continued) ACTIVITY: Evaluating a Function Work with a partner. Consider the function ( ) = +. f f() = + Locate the points (, f ()) on the graph. Eplain how ou found each point. a. (, f ( ) ) b. (, f ( ) ) ( ) c., f () d. (, f ( ) ) ACTIVITY: Comparing Graphs of Functions Work with a partner. The graph of a function from trigonometr is shown at the right. Use the graph to sketch the graph of each function. Eplain our reasoning. = f() a. g ( ) = f( ) + b. g ( ) = f( ) + c. g ( ) = f( ) d. g ( ) = f( ) Big Ideas Math Algebra Copright Big Ideas Learning, LLC

19 Name Date. Function Notation (continued) What Is Your Answer?. IN YUR WN WRDS How can ou use function notation to represent a function? How are standard notation and function notation similar? How are the different? Standard Notation Function Notation = + f( ) = +. Use what ou discovered in Activit to write a general observation that compares the graphs of ( ) ( ) = f and = f + c. Copright Big Ideas Learning, LLC Big Ideas Math Algebra

20 Name Date. Practice For use after Lesson. Find the value of so that the function has the given value.. g ( ) = 8 ; g ( ) =. v ( ) v ( ) = ; =. k ( ) = + 7; k ( ) =. j ( ) j ( ) = + 9; = 8 Graph the linear function.. f( ) = +. h ( ) = 7. You have $. You earn $ each time ou mow our neighbor s lawn. The function s ( ) = + represents our total savings. a. What will our savings be after ou mow times? b. How man times do ou have to mow to save a total of $? Big Ideas Math Algebra Copright Big Ideas Learning, LLC

21 Name Date Etension. Practice For use after Etension. Graph the function. Describe the domain and range.., if =, if >., if = +, if >., if =, if < <, if., if = +, if <, if >. Write a piecewise function for the graph. Copright Big Ideas Learning, LLC Big Ideas Math Algebra

22 Name Date Etension. Practice (continued) Graph the function. Compare the graph to the graph of = the domain and range.. = 7. = +. Describe 8. = 9. = Write an equation for the given translation of =.. units right. units down and 8 units left Big Ideas Math Algebra Copright Big Ideas Learning, LLC

23 Name Date. Comparing Linear and Nonlinear Functions For use with Activit. Essential Question How can ou recognize when a pattern in real life is linear or nonlinear? ACTIVITY: Finding Patterns for Similar Figures Work with a partner. Complete each table for the sequence of similar rectangles. Graph the data in each table. Decide whether each pattern is linear or nonlinear. a. Perimeters of Similar Rectangles b. Areas of Similar Rectangles P A P A Copright Big Ideas Learning, LLC Big Ideas Math Algebra

24 Name Date. Comparing Linear and Nonlinear Functions (continued) ACTIVITY: Comparing Linear and Nonlinear Functions Work with a partner. The table shows the height h (in feet) of a falling object at t seconds. Graph the data in the table. Decide whether the graph is linear or nonlinear. Compare the two falling objects. Which one has an increasing speed? a. Falling parachute jumper b. Falling bowling ball t h 8 7 t h 8 h Parachute Jumper h Bowling Ball Height (feet) 8 Height (feet) Time (seconds) t Time (seconds) t Big Ideas Math Algebra Copright Big Ideas Learning, LLC

25 Name Date. Comparing Linear and Nonlinear Functions (continued) What Is Your Answer?. IN YUR WN WRDS How can ou recognize when a pattern in real life is linear or nonlinear? Describe two real-life patterns: one that is linear and one that is nonlinear. Use patterns that are different from those described in Activities and. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7

26 Name Date. Practice For use after Lesson. Graph the data in the table. Decide whether the function is linear or nonlinear... Does the graph represent a linear or nonlinear function? Eplain.... The table shows the area of a square with side length inches. Does the table represent a linear or nonlinear function? Eplain. Side Length, Area, A 9 8 Big Ideas Math Algebra Copright Big Ideas Learning, LLC

27 Name Date. Arithmetic Sequences For use with Activit. Essential Question How are arithmetic sequences used to describe patterns? ACTIVITY: Describing a Pattern Work with a partner. Use the figures to complete the table. Plot the points in our completed table. Describe the pattern of the -values. a. n = n = n = n = n = Number of Rows, n Number of Dots, 8 n b. n = n = n = n = n = Number of Stars, n Number of Sides, n Copright Big Ideas Learning, LLC Big Ideas Math Algebra 9

28 Name Date. Arithmetic Sequences (continued) c. n = n = n = n = n = n Number of Circles, n ACTIVITY: Using a Pattern in Science to Predict Work with a partner. In chemistr, water is called H because each molecule of water has hdrogen atoms and ogen atom. Use the figures to complete the table. H H H Molecule of Water Describe the pattern of the -values. Use our pattern to predict the number of atoms in molecules. n = n = n = n = n = Number of Molecules, n Number of Atoms, Big Ideas Math Algebra Copright Big Ideas Learning, LLC

29 Name Date. Arithmetic Sequences (continued) ACTIVITY: Writing a Stor Work with a partner. Describe the pattern in the table. Write and illustrate a stor using the numbers in the table. Graph the data shown in the table. Jan Feb Mar Apr Ma Jun Jul Aug Sep ct Nov Dec What Is Your Answer?. IN YUR WN WRDS How are arithmetic sequences used to describe patterns? Give an eample from real life. Copright Big Ideas Learning, LLC Big Ideas Math Algebra

30 Name Date. Practice For use after Lesson. Write the net three terms of the arithmetic sequence.. First term:. First term: Common difference: Common difference:. Find the common difference of the arithmetic sequence.., 8,,,.., 7, 7.7, 8.,.,, 8,, Write the net three terms of the arithmetic sequence..,, 9, 8, 7. 8, 9, 9, 9,... 8.,,,, Determine whether the sequence is arithmetic. If so, find the common difference. 9.,,,,.,,,,.... An amusement park charges $ per person for admission. A season pass costs $ per person. a. Write the first five terms of an arithmetic sequence that represents the total cost of admission for the number of visits in a season. b. How man times does a person have to visit the park for a season pass to be the better deal? Eplain. Big Ideas Math Algebra Copright Big Ideas Learning, LLC