What are the domain and range of the function f(x)= 4 - 2x^2-4

A.) domain: all real numbers
range: all real numbers greater than or equal to –5

B.) domain: all real numbers
range: all real numbers greater than or equal to –4

C.) domain: all real numbers between –2.5 and 2.5
range: all real numbers

D.) domain: all real numbers between –2.5 and 2.5
range: all real numbers greater than or equal to –5

If  you meant to type  f(x) =  (4 - 2x)^2 - 4,  then choose choice B.) domain: all real numbers

range: all real numbers greater than or equal to –4

With your typo... the choices narrow down to choice B and A.  .  The domain is definitely all real numbers for a quadratic function.

Step-by-step explanation:

We have a quadratic function  

f(x) =4  -2*x^2  - 4

I assume there is a typo here.

check   y >= -5  and y >= -4...

what if   f(x) = (4 - 2x)^2  - 4

then  f(x) = 4*(x - 2)^2 - 4   with vertex at  (2, -4)  which makes sense with the answer choice B.)

f(x) = 4*(xx - 4x + 4)  - 4  =  4xx - 16x + 16 -4  = 4xx - 16x +12 ...