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
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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
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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.
