Question

(F(x) = 2|x + 2| - 8), what is the domain of (f) and what is the parent function of the domain?

a) Domain: All real numbers; Parent function: (y = |x|)
b) Domain: All real numbers; Parent function: (y = x)
c) Domain: ([-2, infty)); Parent function: (y = |x|)
d) Domain: ((-2, infty)); Parent function: (y = x)

Answer 1

The domain of the function f(x) = 2|x + 2| - 8 is all real numbers. The parent function of the domain is y = |x|.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For the function f(x) = 2|x + 2| - 8, because it includes an absolute value of a linear term, the function is defined for all real numbers. This is because no matter what value x takes, the expression inside the absolute value will always yield a non-negative number, and thus f(x) will also yield a real number as its output.

The parent function for f(x) in this case is y = |x|. The presence of the absolute value in f(x) indicates that its parent function is the basic absolute value function, which is a V-shaped graph showing distance from zero on the y-axis for any given x-value.

Therefore, the correct answer is: Domain: All real numbers; Parent function: y = |x|. Which corresponds to option (a).