Part 1 {20 points]: Use a graphing calculator or software to guide you in hand-sketching the following functions over an interval that will show the contrast in complexity for each. This graph should use different colors to distinguish one function from the other. Function 1: (26.10g(n)) 2 12 Function 2: 113103 (11 ) First, change the growth {y} axis to show how it makes a difference between observing the behavior of each function for relatively small values to very large values. Then change the size (x) axis from relatively small values to very large values and observe how there can be a perceived difference. Analyze these differences and write a 250 word summary of your observations. Part 2 [5 points}: Introduce a new, third function and graph this function in a new hand-sketched graph which contains all three functions (this new function and the previous two functions observed in Part 1). Answer the following questions: 1. How does this function fit among the previous two functions? Explain how. 2. Which of the two initial functions is its upper-bound? Explain why. 3. Which of the two initial functions is its lower-bound? Explain why. 4. From question 2. and 3., give the appropriate complexityfgrowth terminology for these hounds (Le. Big-0h, or Big-Omega). 5. Can you describe these three functions using Big-Theta, or is this not possible? Explain