Use piecewise and absolute value functions to graph the relationships and analyze the domain and range in each scenario. It's algebra 1

Unit 9 Performance Assessment Savannah's dog, Berta, loves to play in a little wading pool to cool off in the summer. Berta runs and jumps into the pool with muddy feet and gets a lot of dirt in the pool. Savannah decides to empty the pool, clean out the mud, and then refill the pool. The pool contains 72 gallons of water. She drains the pool until it is empty at a rate of 3 gallons per minute, cleans the pool for 12 minutes, and then refills the pool at 3 gallons per minute. 1. Graph the number of gallons of water (G) in the pool over time (t). 80 60 40 20 2. Write a piecewise function to model G(t). 3. What is the domain of G(t)? 4. What is the range of 605)? 5. What is the value of C(15)? What does C(15) mean in this context? Savannah started to wonder how she could speed up this project. She imagines that she could drain and fill the pool twice as fast (6 gallons per minute) and that she didn't have to clean it all. 6. Write the piecewise function and draw the graph of H (r), the new function that Savannah imagines. 80 60 40 20 7. Rewrite HOE) as an absolute value function. 8. Savannah started to wonder about the functions she was writing. When she wrote one function that was increasing, like fo) : 2x 7, and then another function that is decreasing at the same rate like g(x) = 2x + 7, it seemed to Savannah that those two functions might be inverses of each other. Are fx) and 90:6) inverse functions? Explain why or why not. 9. Ifthe filling ofthe pool could be modeled by 6&3 = (t 5)2 in the interval [5,85], what function could you write for 616)? 10. What is the domain of 6105)? 11. What is the range of 6103