The function g is defined by \(\mathrm{g(x) = -x + 8}\). What is the value of \(\mathrm{g(0)}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{g(x) = -x + 8}\)
  • Need to find: \(\mathrm{g(0)}\)
• What this means: substitute \(\mathrm{x = 0}\) into the function expression

2. TRANSLATE the substitution process

• Replace every x in the expression with 0
• \(\mathrm{g(0) = -(0) + 8}\)

3. SIMPLIFY the arithmetic

• \(\mathrm{g(0) = -0 + 8 = 0 + 8 = 8}\)

Answer: 8 (Choice D)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misreading the function definition as \(\mathrm{g(x) = x + (-8)}\) instead of \(\mathrm{g(x) = -x + 8}\)

Students sometimes struggle with negative signs in function expressions and may interpret "-x + 8" as "x + (-8)". If they make this error, their calculation becomes \(\mathrm{g(0) = 0 + (-8) = -8}\).

This may lead them to select Choice A (-8).

Second Most Common Error:

Conceptual confusion about function notation: Not understanding the difference between the input value and the output value

Some students see "find \(\mathrm{g(0)}\)" and think the answer should be 0 because that's the number inside the parentheses. They confuse the input (0) with the output (what \(\mathrm{g(0)}\) equals).

This may lead them to select Choice B (0).

The Bottom Line:

Function evaluation problems require careful attention to negative signs and a clear understanding that \(\mathrm{g(0)}\) asks for the output value when \(\mathrm{x = 0}\), not the input value itself.