Please provide solutions so I can better explain ito my child. Thank you

Lab 3 Supplement IES1 et if ()= %}f'% (2) Analyze lim f(s), lim f(z), lim f(z), ond lim f(x). (b) Identify and describe any points of discontinuity of f(z) over the interval (oco, o). (c) Describe how the graph of f(z) will appear at the points z = 0 and z = 2. 2. Let f(z) = Lzpei=a' (a) Analyze zango f(z) and zEIPoo f(z). (b) Find the equation of any asymptotes that exist. 3. Prove that the absolute value function f(z) = |z| is continuous for all values of z using the continuity checklist. 4. Evaluate Ili)nolo f(z) and z_1411_11\"' f(z) for the following functions. Identify the equation of the borizontal or slant asymptotes when they exist. () fl@)=1e2 (b) f(z) = iz (O f=)= == (d) f(z)==petlo 65z 5. Emilia makes the claim that the function f(z) = J%l violates the Intermediate Value Theorem since she knows that f(2) = 1 and f(2) = 1 but she is not able to find any value between 2 and 2 such that f(c) =0. (a) What does Emilia understand about the Intermediate Value Theorem? (b) Is Emilia correct in her conclusion that f(z) violates the IVT? (c) Graph the function f(z) = J%I- What interesting feature(s) do you notice? (d) What two questions might you pose to Emilia to help her understand the problem more clearly? Lab 4 Preparation 1. Consider the function f(z) = z2. (a) Calculate the average rate of change of f from 1 to b for the following values of b. i. b=2:b=1.5;b=1.1;b=1.01;5=1.001 ii. b=0;b=05;b=0.9;b=0.99;b = 0.999 (b) Based on your answers to part (a) make a hypothesis of what you see happening to the average rate of change as b approaches 1