Respuesta :

Answer:

D is correct

Step-by-step explanation:

f(x) = |x| is f(x) = x for x >= 0 and f(x) = -x for x < 0

Hence:

f(x) = |x + 8| is f(x) = x + 8 when x + 8 >= 0 i.e. x > -8 and

f(x) = -x - 8 when x + 8 < 0 i.e. x < -8

The function having an algebraic expression inside absolute value symbols is known as an absolute functional form, and the calculation is as follows:

Absolute value calculation:

  • An absolute functional form has an algebraic expression inside absolute value symbols.
  • Remember that a number's absolute value is its distance from zero on the number line.

            [tex]\to f(x) = |x|[/tex] is [tex]f(x) = x[/tex] for [tex]x > = 0[/tex] and [tex]f(x) = -x[/tex] for [tex]x < 0[/tex]

          Hence:

           [tex]\to f(x) = |x + 8|[/tex] is [tex]f(x) = x + 8[/tex] when [tex]x + 8 > = 0[/tex] i.e. [tex]x > -8[/tex] and

            [tex]\to f(x) = -x - 8[/tex] when [tex]x + 8 < 0[/tex] i.e. [tex]x < -8[/tex]

Find out more about the absolute value here:

brainly.com/question/1301718