Let's Dance! Portfolio Worksheet PRECALCULUS A Directions: Animation design is something that is used in every cartoon film you've seen, every flip-book you've thumbed through, and every picture you've zoomed in on with your phone. Mathematics plays a key role in these things you enjoy on a regular basis. For full credit on this portfolio, please fill in parts 1, 2, and 3. Make sure that the following are included in your response: 1. All tables are complete, and mathematical calculations are accurate. 2. The answers to each question are filled in completely. Follow the Dancing Robot Use the graph of f (x)=x and transformations to animate the robot dancing. 107 f(x) = 23 5- -10 -5(1, -1)2 0. 0) 5 10 -5 -10-Part 1: Charting the Robot's Dance Moves Complete the table to fill in the missing values that describe the transformation that needs to take place. Would the transformation be a rotation, reflection, translation, or dilation? What type of What would the new equation transformation be? (based on the original would this be? equation of f(x) = x ) Jump straight up 4 units. Move to the left 2 units. Flip his arms (move his right arm up and his left arm down). Spread his arms twice as wide.Part 2: Creating Your Own Dance Story The robot wants to create a dance that takes him from his starting position in the first picture to his ending in the second picture. 107 f(x) = 23 5- (1, 1) -10 -5 (-1, -1). 10, 0) 5 10 -5- J.10- 10 5- 2 ( 0 0) (2, 0.5). (4, 1.5) 0- 3, 1) X -10 -5 5 10 -5 -10-1. Complete the table. Describe the combination of transformations of f (x) =x that would take the dancing robot from his starting position to his ending position. Transformation Description 1st transformation 2nd transformation 3rd transformation 2. Using the original graph of f (x) = x, what would the resultant equation be after all of the transformations you chose in question 1 have taken place? 3. Is there more than one way to get the robot from the first picture to the second? Why or why not? Make sure to justify your reasoning. Part 3: Extending the Idea 1. If you wanted to model movements with both of the robot's arms in the air, what function would you choose as the original model? Could you still do the same transformations with this new equation? 2. Using any power function of your choice, create your own dance for the robot. Make sure you include three to five dance moves. Graph and provide the transformation equation for each.