1) Since the starting point is those inequalities in the standard form, we need to perform some algebraic manipulations to get them in the slope-intercept form
2) So, let's rewrite them by adding/subtracting and dividing/multiplying terms to isolate the y-term on the left:
And the second inequality:
3) Examining the options, we can tell that the answer is:
Thus, the answer is the second option (top to bottom).
F(x)=-4(8)-5=
F(x)=-32-5=
F(x)=-37
Now let's examine the statements:
A)The functions have the same range:FALSE the range changed from y ≥ 0 to y ≤ 0
B)The functions have the same domains. FALSE the doman changed from x ≥ 0 to x ≤ 0
C)The only value that is in the domains of both functions is 0. TRUE: the intersection of x ≥ 0 with x ≤ 0 is 0.
D)There are no values that are in the ranges of both functions. FALSE: 0 is in the ranges of both functions.
E)The domain of g(x) is all values greater than or equal to 0. FALSE: it was proved that the domain of g(x) is all values less than or equal to 0.
F)The range of g(x) is all values less than or equal to 0. TRUE: it was proved above.