Question

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

Answer 1

option D

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 ]