Name Class Date. To translate three units to the left, 3 from the -coordinate. To translate two units down, 2 from the -coordinate.

Transcription

1 Name Class Date 1-1 Eploring Transormations Going Deeper Essential question: What patterns govern transormations o unctions? 1 F-BF.2.3 EXPLORE Translating Points Translate the point (-2, 5) three units to the let and two units down. To translate three units to the let, 3 rom the -coordinate. To translate two units down, 2 rom the -coordinate. Translating (-2, 5) three units to the let and two units down results in the point. 1a. When ou translate a point let or right, how do ou change the coordinates o the point? 1b. When ou translate up or down, how do ou change the coordinates o the point? 2 F-BF.2.3 EXAMPLE Translating a Function Translate the graph o () three units to the let. () Chapter 1 5 Lesson 1

2 2a. How do the -coordinates o the points on the graph change ater being shited to the let? 2b. How do the -coordinates change ater being shited to the let? 3 F-IF.2.5 EXAMPLE Relecting a Function Relect the graph o () across the -ais. 3a. Fill in the table to show how points on the graph o change ater the graph is relected over the -ais. Original Function (-7, 1) (-4, -1) (0, 6) (5, -1) Transormation 3b. How do the -coordinates o the points change ater being relected over the -ais? 3c. How do the -coordinates o the points change ater being relected over the -ais? Chapter 1 6 Lesson 1

3 4 F-BF.2.3 EXAMPLE Stretching or Compressing a Function Consider the transormations (, ) (2, ) and (, ) ( 1 2, ). You will use the tables below to see the eects o these transormations on the graph o () = 2. Complete the table with values o 2 and 1 that correspond to the given values o. 2 2 = = The graph o () = 2 is shown on the grids. Plot the points (2, ) rom our table on the coordinate grid on the let. Connect them with a smooth curve. Do the same or the points ( 1 2, ) on the coordinate grid on the right. 4a. A transormation o the orm (, ) (a, ) is a horizontal stretch or compression. Based on the graphs above, or what kinds o numbers a do ou think that the transormation (, ) (a, ) is a horizontal compression? 4b. For what kinds o numbers a do ou think that the transormation (, ) (a, ) is a horizontal stretch? Chapter 1 7 Lesson 1

4 PRACTICE Perorm the given translation on the point (5, -3) and give the coordinates o the translated point units right 2. 2 units up 3. 1 unit right, 7 units down Use a table to perorm each transormation o = (). 4. translation 4 units up Original Function Transormation (-5, 2) (-4, -1) (1, -1) (3, 3) (7, 3) 5. relection across the -ais Original Function Transormation (-5, 0) (-3, 3) (0, 0) (2, -2) (6, 2) 6. horizontal stretch b a actor o 4 Original Function Transormation (-4, 8) () (-1, 2) (0, 0) (2, 2) (4, 4) Chapter 1 8 Lesson 1

5 Name Class Date 1-1 Additional Practice Perorm the given translation on the point (2, 5) and give the coordinates o the translated point. 1. let 3 units 2. down 6 units 3. right 4 units, up 2 units Use the table to perorm each transormation o = (). Use the same coordinate plane as the original unction. 4. translation let 1 unit, down 5 units 5. vertical stretch 6. horizontal compression 7. relection across -ais actor o actor o Solve. 8. George has a goal or the number o computers he wants to sell each month or the net 6 months at his computer store. He draws a graph to show his projected proits or that period. Then he decides to discount the prices b 10%. How will this aect his proits? Identi the transormation to his graph and describe how to ind the ordered pairs or the transormation. Chapter 1 9 Lesson 1

6 Problem Solving Harr is working on a budget or a concert. The graph shows the total cost o renting the hall. A cleaning ee o $40 or each rental is included in the graph. Use the graph or Eercises What is the cost o renting the hall or 2 hours? or 3 hours? or 6 hours? or 7 hours? 2. What is the rate per hour not including the cleaning ee i Harr rents the hall or up to 3 hours? 3. What is the rate per hour ater the irst 3 hours? 4. Describe the eect on the graph i the cleaning ee were changed to $ The managers decide that the minimum time or which the hall can be rented is 3 hours. Describe the eect this change would have on the graph above. How would the range change? Choose the letter or the best answer. 7. Martha s proits rom her bagel store last ear were $0.35 per dozen bagels sold. This ear her proits decreased 10%. What kind o transormation does this represent? A vertical compression B vertical stretch C horizontal compression D none o the above 6. The Art Center gives Harr a graph showing its charges. This graph is the same shape as the graph above, but ever point has been translated up 10 units. What would be the eect on Harr s budget i he chose to have the concert at the Art Center? 8. Shana drew the graph or a quadratic unction. Then she did a horizontal stretch o the curve. Which transormation did she perorm? F (, ) (, a); a > 1 G (, ) (b, ); 0 < b < 1 H (, ) (, a); 0 < a < 1 J (, ) (b, ); b > 1 Chapter 1 10 Lesson 1