The function g is defined by \(\mathrm{g(x) = |x + 18|}\). What is the value of \(\mathrm{g(4)}\)?

1. TRANSLATE the question into mathematical action

• The question asks for \(\mathrm{g(4)}\), which means:
  • Substitute \(\mathrm{x = 4}\) into the function \(\mathrm{g(x) = |x + 18|}\)

2. SIMPLIFY through substitution

• Replace x with 4 in the function:
  \(\mathrm{g(4) = |4 + 18|}\)

3. SIMPLIFY the arithmetic inside the absolute value bars

• Calculate the sum:
  \(\mathrm{g(4) = |22|}\)

4. SIMPLIFY by applying the absolute value

• Since 22 is positive, \(\mathrm{|22| = 22}\)
• Therefore: \(\mathrm{g(4) = 22}\)

Answer: D. 22

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Making basic arithmetic mistakes when calculating \(\mathrm{4 + 18}\), possibly getting 14 instead of 22.

If a student calculates \(\mathrm{4 + 18 = 14}\), they would get \(\mathrm{g(4) = |14| = 14}\), leading them to select Choice C (14).

Second Most Common Error:

Conceptual confusion about absolute value: Thinking that absolute value can sometimes be negative, particularly when they see the "+18" and incorrectly associate it with making things negative.

This confusion might lead them to incorrectly think the answer should be negative, causing them to select Choice A (-18) or get confused and guess.

The Bottom Line:

This problem tests whether students can systematically work through a multi-step evaluation without making careless arithmetic errors or misunderstanding the absolute value operation on positive numbers.