For each of the following sets, prove whether they are convex or not. 1. Given a collection of n = N convex sets {S}"ï±1, S := 2. Given p > 0, S := {x = Rd : ||x||₂ = 1}. € i=1' ±1 Si. i=1 3. Given p≥ 1, S := {{a¡};£1, a¡ € R : (Σºº1₁ |ai|P)½³ < ∞0}.

Two sets A and B are defined as follows: A = {x, y, z}; B = {1, 2, 3}. y● Og Oh y● f 20 ●3 ●3 (a) Which of the rules displayed in the figures represent functions from A to B? (Select all that apply.) Of (b) For each rule that does represent a function, specify the range. (If the rule does not represent a function, enter NOT A FUNCTION.) range of f } { range of g { range of h {

Match these values of r with the accompanying scatterplots: 1, -0.355, -0.718, 0.355, and 0.996. Scatterplot 1 Scatterplot 2 8- 6- 6- FUUS 4- 2-* 0- 0 0.2 0.4 0.6 0.8 1 X 4- 2- 0- 0 0.2 0.4 0.6 0.8 X > 15- 14- 13- 12- 11- Scatterplot 3 10+ . 0 0.2 0.4 0.6 0.8 X O A. Scatterplot 1, r=-0.355; Scatterplot 2, r = 1, Scatterplot 3, r = 0.355, Scatterplot 4, r = -0.718, Scatterplot 5, r = 0.996 B. Scatterplot 1, r = 0.355; Scatterplot 2, r = 0.996, Scatterplot 3, r = -0.355, Scatterplot 4, r = -0.718, Scatterplot 5, r = 1 O C. Scatterplot 1, r=-0.355; Scatterplot 2, r = 0.996, Scatterplot 3, r = 0.355, Scatterplot 4, r = -0.718, Scatterplot 5, r = 1 O D. Scatterplot 1, r= 0.355; Scatterplot 2, r = 1, Scatterplot 3, r = -0.355, Scatterplot 4, r = -0.718, Scatterplot 5, r = 0.996 8- 6- 4- 2- Scatterplot 4 0- 0 0.2 0.4 0.6 0.8 X 8- 6- 4- 2- 04 0 Scatterplot 5 . • 0.2 0.4 0.6 0.8 X ..

1. Find the GLB of the set: {x: x – 4 < 1}. -1 b. 1 -3 d. 3 e. 0 а. с.