Question

Use the graphs to determine the values of x for which both f(x) and g(x) are decreasing.

(g(x) is going up
f(x) is going down



A)
{x|x<−4}




B)
{x|−4<x<−2}



C)
{x|−2<x<0}



D)
{x|0<x<2.5}

Answer 1

To determine the intervals where both \( f(x) \) and \( g(x) \) are decreasing, we need to focus on the behavior of the graphs of both functions.

If \( g(x) \) is increasing, it means that there are no intervals where \( g(x) \) is decreasing. Thus, for any value of \( x \) where \( g(x) \) is increasing, it does not meet the criteria that both \( f(x) \) and \( g(x) \) are decreasing.

Since you mentioned that \( g(x) \) is going up while \( f(x) \) is going down, the conditions to satisfy both functions being decreasing cannot be met. All intervals described would lead us to conclude that there are no values of \( x \) such that both functions are decreasing at the same time, because \( g(x) \) is not decreasing on any interval.

Thus, there would be no correct choice among the given options A, B, C, or D.