Question

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 1

Answer:

A

C

D

Step-by-step explanation:

Answer 2

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)