G2+ORQ+Hickey,+Fay,+Grignon

1. Functions: y=2x-2 y=√2x 2. I know that these functions meet the requirements because if you are taking the square root of x then it is impossible for the solution to be negative even if x is negative. Therefore the domain would be all numbers greater then or equal to 0. Also I know that these graphs intersect because the y-intercept of y=2x-2 is below zero so it must cross the second line because it flattens out as x gets larger. 3. 2x-2 ≤ √2x

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5.  2x-2 ≤ √2x (2x-2)^2 = (√2x)^2 4x^2-8x+4 = 2x 4x^2-10x+4 =0 (4x-2)(x-2) 2(2x-2)(x-2) y=2x-2 y=2(2)-2 y=4-2 y=2 y=√2x y=√2(2) y=√4 y=2 intersection point = (2,2)

6. 2x-2 ≤ √2x when 0 ≤ x ≤ 2 so,

[0,2]

7. Using the Intercept of the two lines, (2,2), and the visual of the graph, I know that 2x-2 will only be less than or equal to √2x when x is less than or equal to 2. And because √2x cannot have any negative values because of its nature, i know that 2x-2 will not be greater than √2x when x < 0 since there will be nothing to compare. Therefore, I know that when x is less than 2 but greater than or equal to 0, 2x-2 will be less than √2x, Hence 0 ≤ x ≤ 2 Hence [0,2]