2 LIMITS

GROUP WORK 2, SECTION 2.2The Shape of Things to ComeIn this activity we are going to explore a set of functions:f 1 (x) = xf 2 (x) = x 2f 3 (x) = x 3.f n (x) = x n , n any positive integer1. To start with, let’s practice the new notation. Compute the following:f 1 (2) = f 2 (0.6) = f 3 (0.8) = f 4 (0) = f 8 (1.01) =2. Sketch the functions f 1 , f 2 , f 3 , f 6 ,and f 8 on the set of axes below.3. The number 0 plays a special role, since f n (0) = 0 n = 0foranyn. Find another number a > 0suchthatf n (a) = a for all n.4. We know that limx→0f n (x) = 0foranyn. How is this fact reflected on your graphs above?48