(iv) $g(x) = |x - 5|$

(iv) $g(x) = |x - 5|$

Given:

• Domain ($D_g$): Absolute value is defined for every real number:

  • $g(5) = |5 - 5| = 0$
  • $g(0) = |0 - 5| = |-5| = 5$
  • $g(-3) = |-3 - 5| = |-8| = 8$
  $$\boxed{D_g = \mathbb{R} = (-\infty, \infty)}$$

• Range ($R_g$): The magnitude of a real number is always non-negative:

  $$|x - 5| \ge 0 \implies y \ge 0$$
  • Minimum output is $0$ at vertex $x = 5$.
  • For $y = 4 \implies x = 5 \pm 4 \implies g(9) = 4$ and $g(1) = 4$.
  $$\boxed{R_g = [0, \infty)}$$