Which functions have a maximum value greater than the maximum of the function g (x) = - (x + 3) 2 - 4? Check all that apply. f (x) = - (x + 1) 2 - 2 f (x) = - |x + 4| - 5 f (x) = - |2x| + 3

Answer: f (x) = - (x + 1) ^2 - 2 and f (x) = - |2x| + 3

Step-by-step explanation:

The maximum value of the function

g (x) = - (x + 3) ^2 - 4

we can derivate the function and find the root:

g' = - 2x = 0

then x = 0 give us the maximum value of g (x)

g (0) = - 9 - 4 = - 11

a) f (x) = - (x + 1) ^2 - 2

The maximum value of this function is also at x = 0 (because the construction is the same as before) then the maximum is:

f (0) = - 1 - 2 = 3

This maximum is bigger than the one of g (x)

b) f (x) = - |x + 4| - 5

We have a minus previous to a modulus, so the maximum value will be when whe have the minimum module of x, that is for x = 0, here we have that the maximum is;

f (x) = - I4I - 5 = - 9

Is the same maximum of g (x)

c) f (x) = - |2x| + 3

Same as before, the maximum is at x = 0

f (0) = 0 + 3 = 3

The maximum is bigger than the one of g (x)

A

C

D