Calculus question

Question

G = { (x, y) | y = (x – 2)² + x and x is a positive integer less than 6 }. What is the range of G? 

a. {1, 2, 3, 4, 5}

 b. {2, 4, 8, 14} 

 c. {2, 4, 8, 14, 22} 

 d. {1, 2, 3, 4, 5, 6}

Answer 1

x=1,2,3,4,5

G(1) = (1-2)^2 + 1 = (-1)^2 + 1 = 1+1 = 2

G(2) = (2-2)^2 + 2 = 0^2 + 2 = 0+2 = 2

G(3) = (3-2)^2 + 3 = 1^2 + 3 = 1+3 = 4

G(4) = (4-2)^2 + 4 = 2^2 + 4 = 4+4 = 8

G(5) = (5-2)^2 + 5 = 3^2 + 5 = 9+5 = 14

The range is {2,4,8,14}