Question

I need help with this, please, I'm not really sure what to do to get the answer

Answer 1

Answer:

option D

Step-by-step explanation:

Clearly from the graph we say that at x = 4 and  x = -6, f(x) = 0

Now we will check this with your options.

A) f(x) = (x + 1 )² - 5

     at x = 4, f(x) = 25 - 5 = 20 ≠ 0 ; not A

B)  f(x) = x - 5

    at x = 4, f(x) = 4 - 5 = 1 ≠ 0 ; not  B

C) f(x) = (x + 1 )³ - 5

     at x = 4 , f(x) = 125 - 5 = 120 ≠ 0 ; not C

D) f(x) = | x + 1 | - 5

    at x = 4 , f(x) = | 4 + 1 | - 5

                        = 5 - 5 = 0    ; satisfies

    at x = -6 , f(x) = | - 6 + 1 | - 5

                         = | - 5 | - 5

                         = 5 - 5 = 0  ; D satisfies  [ | - a | =a , absolute value function ]