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Let's take these one at a time. A The A choice is that the y intercept of g(x) < y intercept of f(x). Remember, a y intercept occurs when x = 0 g(x) = 2 * sqrt(x) - 8 g(0) = 2*0 - 8 g(0) = - 8 ======= f(x) = - 4 when x = 0 (you just read it.) - 4 is greater than -8. That's a true statement. Think money. Would you rather be 4 dollars in debt or 8 dollars in debt?  A: True <<<<<< answer for A. B y intercept  occurs when x = 0 The values of f(x) and g(x) have been found in part A. Are they equal? The y intercept of g(x) = g(0) = 2*sqrt(0) - 8 = - 8 The y intercept of f(x) = f(x)  = - 4 when x = 0  Conclusion They are not equal and B is not the answer. C The x intercept occurs when y = 0 g(x) = 0  0 = 2*sqrt(x) - 8 8 = 2*sqrt(x) 4 = sqrt(x) x = 16 ====== When f(x) = 0, x = 16. Conclusion The x intercepts are both 16. This statement is true. C: True <<<<<< answer. D If the condition is anything but equal, the statement is false. g(x) is not greater then f(x). D <<<<<< False.