Lesson 7.1 Secret Codes

Transcription

1 Lesson 7. Secret Codes. Use this table to code each word. Input A B C D E F G H I J K L M Coded output M N O P Q R S T U V W X Y Input N O P Q R S T U V W X Y Z Coded output Z A B C D E F G H I J K L a. ALGEBRA b. EQUATION c. SOLVE. Use this coding grid to decode each word. a. KGUUWJ b. JSVAG c. WAFKLWAF 3. Luisa used a letter-shift code to code her name as TCQAI. a. Write the rule or create the coding grid for Luisa s code. b. Use Luisa s code to decode BWX AMKZMB. 4. Use this coding grid to answer 4a c. a. What are the possible input values? b. What are the possible output values? c. Is this code a function? Eplain wh or wh not. Coded output Coded output X YZ U V W R ST Q O P N M K L H IJ G D EF A B C X YZ U V W R ST Q O P N M K L H IJ G D EF A B C ABCDEFGHI J KLMNOPQRSTUVWXYZ Original input ABCDEFGHI J KLMNOPQRSTUVWXYZ Original input 7 Ke Curriculum Press Discovering Algebra More Practice Your Skills 49

2 Lesson 7. Functions and Graphs. Use the given equations to find the missing output values. a. 3 b..5 3 c Input Output Input Output Input Output Use the given equations to find the missing domain and range values. a. 3 5 b. 3 6 c. Domain Range Domain Range Domain Range Find whether each graph represents a function. a. b. c. d. e. f. 5 Discovering Algebra More Practice Your Skills 7 Ke Curriculum Press

3 Lesson 7.3 Graphs of Real-World Situations. For each relationship, identif the independent variable and the dependent variable. Then sketch a reasonable graph for each situation and label the aes. Write a few sentences eplaining each graph. In our eplanations, use terms such as linear, nonlinear, continuous, discrete, increasing, and decreasing. a. The temperature of a carton of milk and the length of time it has been out of the refrigerator b. The number of cars on the freewa and the level of ehaust fumes in the air c. The temperature of a pot of water as it is heated d. The relationship between the cooking time for a -pound roast and the temperature of the oven e. The distance from a Ferris-wheel rider to the ground during two revolutions. Sketch a graph of a continuous function to fit each description. a. Linear and increasing, then linear and decreasing b. Neither increasing nor decreasing c. Increasing with a slower and slower rate of change d. Decreasing with a slower and slower rate of change, then increasing with a faster and faster rate of change e. Increasing with a slower and slower rate of change, then increasing with a faster and faster rate of change 3. Write an inequalit for each interval in 3a f. Include the least point in each interval and eclude the greatest point in each interval. A B C D E a. A to B b. B to D c. A to C d. B to E e. C to E f. C to D 4. Describe each of these discrete function graphs using the words increasing, decreasing, linear, nonlinear, and rate of change. a. b. c. 7 Ke Curriculum Press Discovering Algebra More Practice Your Skills 5

4 Lesson 7.4 Function Notation. Find each unknown function value or -value for f() 4 7 and g() 3 5 without using our calculator. Then enter the equation for f() into Y and the equation for g() into Y.Use function notation on our calculator to check our answers. a. f() b. f() c. f( 3) d., when f() 3 e. g(6) f. g( 7) g. g(.5) h., when g() 5 i. f(3.5) j. g 3 k., when f() 3 l. 3, when g().9. Find the -coordinate corresponding to each -coordinate or vice versa for the functions f() 4 5 and g() 4(.).Check our answers with our calculator. a. f() b. f( 3) c. f() d. f() e. f(.5) f. g() g. g( ) h., when g() 4 3. Use the graph of f() to answer each question. a. What is the value of f()? 4 b. What is the value of f(3)? f() c. For what -value or -values does f() equal 3? d. For what -value or -values does f() equal? e. What are the domain and range shown on the graph? 7 4. The graph of the function h(t) shows the height of a paper airplane on its maiden voage. a. What are the dependent and independent variables? b. What are the domain and range shown on the graph? c. Use function notation to represent the plane s height after 6 seconds. Height (m) 4 h(t) Time (sec) t d. Use function notation to represent the time at which the plane was 4 meters high. 5. The function f().5.5 represents the distance of a motorized to car from a motion sensor, where distance is measured in meters and time () is measured in seconds. a. Find f(3). Eplain what this means. b. How far is the car from the sensor at time? Epress our answer using function notation. c. When will the car be.5 meters from the sensor? Epress our answer using function notation. 5 Discovering Algebra More Practice Your Skills 7 Ke Curriculum Press

5 Lesson 7.5 Defining the Absolute-Value Function. Find the value of each epression without using a calculator. Check our results with our calculator. a. b. 9 c. 4 3 d. 7 e. 7 f. 6 g. 6 h. 4 3 i. 7 5 j. 8 k l. 3 6 m. 4 5 n. 5 3 o. 3 ( 4)(5). Find the -values that satisf each equation. a. 6 b. 3.4 c. 4.5 d. 3 e. 3 f. 3 5 g. 8 h. 5.5 i Evaluate both sides of each statement to determine whether to replace the bo with,,or.use our calculator to check our answers. 3 a. 7 7 b c. 6 ( 6) d. 5 5 e. ( 3) f. ( 5) g. 4 ( 6) 4 6 h. 3 3 i Find each value if f() 3 and g() 3. a. f( 4) b. f( ) c. f() d. f() e. f(5) f. f(8) g. g( 4) h. g( ) i. g() j. g() k. g(5) l. g(8) m., when f() n., when g() o., when f() 7 p., when g() 7 7 Ke Curriculum Press Discovering Algebra More Practice Your Skills 53

6 Lesson 7.6 Squares, Squaring, and Parabolas. The length of a rectangle is cm greater than the width. a. Complete the table b filling in the missing width, length, perimeter, and area of each rectangle. b. Let represent the width of the rectangle. Use function notation to write an equation for the perimeter. c. Is the relationship between width and perimeter linear? Eplain wh or wh not. d. Let represent the width of the rectangle. Use function notation to write an equation for the area. e. Is the relationship between width and area linear? Eplain wh or wh not. Width Length Perimeter Area (cm) (cm) (cm) (cm ) Find the value of each epression without using a calculator. Check our results with our calculator. a. 4 b. ( 3) c.. d. (.5) e. ( 8) f. 49 g..8 h..44 i. 3 j. 36 k. (.) 3 l. 3. Solve each equation for.use a calculator graph or table to verif our answers. a. 6.3 b. 4 8 c. 6 d. 5 7 e. f. ( 3) 65 g..56 h. 8.9 i. 5 j. 9 3 k. 4 5 l Sketch the graphs of and on the same set of aes. Describe the similarities and differences of the graphs. 54 Discovering Algebra More Practice Your Skills 7 Ke Curriculum Press