Homework 1.1A—Transformations of Linear and Absolute Value Functions Linear Functions and Models
Name: ________________________ Advanced Algebra 2
Date: _________________________ Graph the function and its parent function by hand. Then describe the transformation. 1​. f (x) =− 4
4​. f (x) = |x − 1| + 1
7. f (x) =− |x + 4| + 6
2. ​ f (x) = 23 x + 2
3. f (x) =− 3x − 1 5. f (x) = |x − 2| − 3
6. f (x) = 5|x − 2| − 7 8. f (x) =​ 52 |x − 1| − 4
9**​. f (x) =− | 13 x − 3| Identify the function family to which f belongs. Write an equation of the graph shown. 10. 11. 12. 13. Identify the function family and state the domain and range. Use a graphing calculator to verify your result. a. g(x) = |x + 2| − 1
b. g(x) = 3x + 4 c. g(x) = 7 d. g(x) = |x − 3| + 2 **Note: The following questions require you to explain your answer and/or your reasoning. Explanations must be written in complete sentences and must use correct mathematical terminology (Not sure what I mean here? Check out the terms we defined during the lesson!) You may include graphs or diagrams to clarify your communication.** 14. You want to shoot the eight ball into the corner pocket on a pool table 10 feet long and 5 feet wide. The ball is at (2, 1); the pocket is at (10, 0). You plan to bank off the side at(6, 5). Write an equation for the path of the ball. Do you make your shot? Explain. 15. Your friend says two different transformations of the graph of the parent linear function can result in the graph of f (x) = x − 2 . Is your friend correct? Explain. Name: ________________________ 16. Graph the functions f (x) = |x − 4| and g(x) = |x| − 4 using your graphing calculator. Are they equivalent? Explain. 17. At 8:00 a.m., the temperature is 43℉ . The temperature increases 2℉ each hour for the next 7 hours. Graph the temperatures over time ( t = 0 represents 8:00 a.m.). What type of function can you use to model the data? Explain. Write an equation that models this situation.