Lesson 4.1 Interpreting Graphs

Size: px

Start display at page:

Download "Lesson 4.1 Interpreting Graphs"

Wilfred Eaton
5 years ago
Views:

1 Lesson 4.1 Interpreting Graphs 1. Describe the pattern of the graph of each of the following situations as the graphs are read from left to right as increasing, decreasing, increasing and then decreasing, or decreasing and then increasing. a. The height of a child at birth and on each birthda from age 1 to age b. The height of a ball that is thrown upward from the top of a building from the time it is thrown until it hits the ground. For each of the situations described in Eercise 1, describe the real-world meaning of the vertical intercept of the graph. 3. Sketch a graph to match the description below. Increasing rapidl at a constant rate, then suddenl becoming constant, then decreasing rapidl at a constant rate 4. Sketch what ou think is a reasonable graph for each relationship described. In each situation, identif the variables and label our aes appropriatel. a. The temperature of a hot drink sitting on our desk b. Your speed as ou ccle up a hill and down the other side Discovering Advanced Algebra More Practice Your Skills CHAPTER Ke Curriculum Press

2 Lesson 4. Function Notation 1. Determine whether or not each graph represents a function. Eplain how ou know. a. b. c.. Find each of the indicated function values. a. If f () 4 1, find f 1 _ 4, f (0), f (0.7), f (), and f (1). b. If f (), find f ( 4), f (0), f (), f (8), and f (4) Use the graph at right to find each of the following. a. f (3) f ( 3) b. f (f (10)) c. when f () 3 d. when f ( 3) 3 4. Define variables and write a function that describes each situation. a. You drive on an interstate highwa with our cruise control set at miles per hour and do not need to stop or alter our speed. b. You rent a small moving van to move our belongings to our new apartment. The rental compan charges $4 a da plus $0. a mile to rent the van. 0 CHAPTER 4 Discovering Advanced Algebra More Practice Your Skills 010 Ke Curriculum Press

3 Lesson 4.3 Lines in Motion 1. Describe how each graph translates the graph of f (). a. f () 3 b. f ( ) c. f ( 7). Find each of the following. a. f ( ) if f () 4 b. 3 f ( 4) if f () c. f ( ) if f () 1 d. 3 f ( ) if f () 8 3. Write an equation for each line. a. The line 1. translated right 3 units b. The line translated up units and left units c. The line 1 _ translated down 1 unit and right 4 units 4. The graph of f () is shown at right. Write an equation for each related graph showing how the function has been translated. a. b. c. d Discovering Advanced Algebra More Practice Your Skills CHAPTER Ke Curriculum Press

4 Lesson 4.4 Translations and the Quadratic Famil 1. Describe the translations of the graph of needed to produce the graph of each equation. a. b. ( ) c. ( 3) 9. Find the verte of each parabola. a. 3 b. ( ) c. 8 ( ) 3. Each parabola described is the graph of. Write an equation for each parabola and sketch its graph. a. The parabola is translated horizontall 3 units. b. The parabola is translated verticall 1 unit. c. The parabola is translated horizontall units and verticall 3 units. 4. Describe what happens to the graph of in the following situations. a. is replaced with ( 1). b. is replaced with ( ).. Solve. a. 31 b. 1 c. ( 3) 100 d. ( 7) 144 e. ( 4) 31 f. 0 ( ) 3 CHAPTER 4 Discovering Advanced Algebra More Practice Your Skills 010 Ke Curriculum Press

5 Lesson 4. Reflections and the Square Root Famil 1. Describe what happens to the graph of in each of the following situations. a. is replaced with ( ). b. is replaced with ( ). c. is replaced with ( 1). d. is replaced with ( 8).. Each graph below is a transformation of the graph of either the parent function or the parent function. Write an equation for each graph. b. e. f. a. c. d. 3. Given the graph of f () at right, draw a graph of each of these related functions. a. f () b. f ( ) c. f ( ) Discovering Advanced Algebra More Practice Your Skills CHAPTER Ke Curriculum Press

6 Lesson 4. Dilations and the Absolute-Value Famil 1. Each graph is a transformation of one of the parent functions ou ve studied. Write an equation for each graph. c. d. b. a.. Describe the transformations of the graph of needed to produce the graph of each equation. a. 3 b c Find the verte of the graph of each equation in Eercise and sketch the graph. 4. Solve. a. 7 0 b c. 1. Solve each equation for. a. 4 3 b. ( 1) c CHAPTER 4 Discovering Advanced Algebra More Practice Your Skills 010 Ke Curriculum Press

7 Lesson 4.7 Transformations and the Circle Famil 1. Write an equation for each circle. b. e. a. c. d.. If f () 1, write an equation for each of the following related functions. a. f () b. f ( ) c. f () d. f () 3. Without graphing, find the - and -intercepts of the graph of each equation. a. 1 b. 1 c. 1 () d. 1 (4) e. 1 3 f Write an equation for each transformation of the unit circle, and identif its graph as a circle or an ellipse. Then sketch the graph. a. Replace with _ and with _. b. Replace with _ 4 and with _ 3. Discovering Advanced Algebra More Practice Your Skills CHAPTER Ke Curriculum Press

8 Lesson 4.8 Compositions of Functions 1. The functions f and g are defined b sets of input and output values. f {(, 0), ( 1, 1), ( 3, 4), (1, ), (3, 4), (, )} g {(4, 1), (0, ), (1, 1), (, ), (, 0)} a. What is the domain of f? b. What is the range of g? c. Find f (g (4)). d. Find g (f ( 3)). e. Find f (g (f ())). f. Find g (f (g (0))).. Use these three functions to find each value: f () 3, g () ( ), h() 4. a. g () 1 b. h(f (7)) c. h(g (f (0))) d. g (h(a)) 3. Marla, Shamim, and Julie went out for dinner together. The sales ta on the meal was %, and the agreed to leave a 1% tip. Marla thought the should calculate the tip b finding 1% of the total bill, including the sales ta. Shamim thought the should calculate the tip b finding 1% of the bill before the ta was added. Julie thought it wouldn t make an difference. Let represent the cost of the meal in dollars before ta and tip are added. a. Find a function f that gives the cost of the meal, including sales ta but not the tip. b. Find a function g that gives the amount of the tip calculated the wa Shamim suggested. c. Use composition to find a function that gives the amount of the tip calculated the wa Marla suggested. d. If the cost of the meal before ta was $0, find the amount the will leave as a tip, calculated Marla s wa and Shamim s wa. CHAPTER 4 Discovering Advanced Algebra More Practice Your Skills 010 Ke Curriculum Press

9 c. 9 31, a. ( 4, ) b., 3 4 c. ( 0, 10) 4. a. Consistent; independent b. Consistent; dependent c. Inconsistent LESSON 4.1 Interpreting Graphs 1. a. Increasing b. Increasing and then decreasing. a. The child s height at birth b. The height of the top of the building 3. Possible answer: 4. a. Independent variable: time; dependent variable: temperature. Sample graph: Temperature Time b. Independent variable: time; dependent variable: speed. Sample graph: Speed Time c. Not a function. There are -values that are paired with two -values. Also, vertical lines can be drawn that cross the graph more than once.. a. f 1 4 0, f (0) 1, f (0.7), f () 3, f (1) 7 b. f ( 4) 1 1, f (0), f (), 4 f (8) 1, f (4) a. 10 b. 13 c. 0. d a. If t is the time driven and d is the distance driven, then d t. b. If m is the miles driven, d is the number of das the van is rented, and c is the cost of renting the van, then c 4d 0.m. LESSON 4.3 Lines in Motion 1. a. Down 3 units b. Left units c. Right 7 units and up units. a. 4( ) 4 8 b. 3 ( 4) 11 c. ( ) 1 9 d. 3 8 ( ) 3. a. 1.( 3), or b. ( ), or 3 c. 1 1 ( 4), or a. f () b. 3 f () c. f ( 3) d. 3 f ( ) LESSON 4.4 Translations and the Quadratic Famil 1. a. Verticall units b. Horizontall units c. Horizontall 3 units and verticall 9 units. a. (0, 3) b. (, 0) c. (, 8) 3. a. ( 3) b. 1 9 LESSON 4. Function Notation 1. a. Function. Each -value has onl one -value. Also, no vertical line crosses the graph more than once b. Not a function. There are -values that are paired with two -values. Also, vertical lines can be drawn that cross the graph more than once. 90 ANSWERS Discovering Advanced Algebra More Practice Your Skills 010 Ke Curriculum Press

10 c. ( ) 3 3. a. (3, 0) b. (0, 0) 4 4. a. Translated verticall 1 unit c. (1, ) b. Translated horizontall units. a. or b. 8 or 8 c. 13 or 7 d. or 19 e. or 10 f LESSON 4. Reflections and the Square Root Famil 1. a. Translated horizontall units b. Translated verticall units c. Translated verticall 1 unit d. Translated horizontall 8 units. a. 3 b. 4 c. 4 d. ( ) e. f. ( ) 3 3. a. c. 7 3 b. 3 LESSON 4. Dilations and the Absolute-Value Famil 1. a. 3 4 b. 3 1 c. 3 d. ( ) 4. a. Horizontal translation 3 units b. Vertical dilation b a factor of 1. and horizontal dilation b a factor of c. Vertical dilation b a factor of ; horizontal translation 1 unit and vertical translation 4 units 4. a. 1 or b. 9 or 1 c. 14 or 14. a. 4 b. ( 1) 3 c. 3 1 LESSON 4.7 Transformations and the Circle Famil 1. a. 4 b. c. ( ) 1 d. ( 3) 9 e. ( 4) ( 1) 4. a. f () 1 b. f ( ) 1 c. f () 1 d. f () 1 () a. -intercepts: 1, 1; -intercept: 1 b. -intercepts: 1, 1; -intercept: c. -intercepts: 0., 0.; -intercept: 1 d. -intercepts: 0., 0.; -intercept: e. -intercepts: 3, 3; -intercept: 1 f. -intercepts: 4, 4; -intercept: 4. a. 1; b ; circle ellipse Discovering Advanced Algebra More Practice Your Skills ANSWERS Ke Curriculum Press

11 LESSON 4.8 Compositions of Functions 1. a. { 3,, 1, 1, 3, } b. {, 1, 0} c. 1 d. 1 e. f. 0. a. ( ) b. 0 c. 8 d. a 4 4a 4 3. a. f () 1.0 b. g () 0.1 c. g (f ()) 0.1(1.0) 0.19 d. Marla s wa: $7.9; Shamim s wa: $7.0 LESSON.1 Eponential Functions 1. a. r (8) b. j (10) a. a 1 9., a 7.8, a 3.144; 1(0.8) b. u , u.70, u ; 0.(.1) 3. a. f (0) 000, f (1) 1800, f () 10; u 0 000, u n 0.9u n 1 where n 1; eponential deca b. f (0) 3000, f (1) 3003, f () ; u , u n 1.001u n 1 where n 1; eponential growth c. f (0) 0.1, f (1) 0.0, f () 0.0; u 0 0.1, u n 0.u n 1 where n 1; eponential deca 4. a. 0.7; decrease of % b. 0. _ 8 ; decrease of 11. _ 1 % c. 1.; increase of 0%. a. u , u n 0.84u n 1 where n 1 b. Let represent the number of ears after the car was purchased and represent the value of the car. 17,00(0.84) LESSON. Properties of Eponents and Power Functions 1. a. 1 9 d. 1 1 b e. 9 c. 1 f a. b. 3 c. 4. a.. b c d e. 1. f LESSON.3 Rational Eponents and Roots 1. a. Power b. Eponential c. Power. a. c 3 b. d 4 3 c. r 3. a. 43 b. 1.9 c d. 3 e f a. 3 3 b. 3 c. ( ) 3 d. 4 ( 3) 3 e. 3 f. 0.( 3) 3 LESSON.4 Applications of Eponential and Power Equations 1. a b. c. 1.4 d..80 e. 0.0 f a. 4 b. 7 9 c. 7 d e f. 3. a. 3.% b. 3.9% 4. a. Let t represent the ear and P represent the population. P 3,000(0.9 ) t 00 b. 1,9 c. 018 LESSON. Building Inverses of Functions 1. a. f : (, 10), (0, 4), 4 3, 0, (4, 8); f 1 : ( 10, ), ( 4, 0), 0, 4 3, (8, 4) b. f : ( 3, 9), ( 1, 3), (, ), (, 13); f 1 : ( 9, 3), ( 3, 1), (, ), (13, ). a. Function; b. Not a function; 1. a. 3 8 b c. 18 d e. 1 1 f. 1 1, or ANSWERS Discovering Advanced Algebra More Practice Your Skills 010 Ke Curriculum Press

Lesson 4.1 Interpreting Graphs

Lesson 4.1 Interpreting Graphs 1. Describe the pattern of the graph of each of the following situations as the graphs are read from left to right as increasing, decreasing, increasing and then decreasing,