Question:The function g is defined by \(\mathrm{g(x) = x - 12}\). What is the value of \(\mathrm{g(9)}\)?-12-339

1. TRANSLATE the problem information

• Given information:
  • Function g is defined by \(\mathrm{g(x) = x - 12}\)
  • Need to find the value of \(\mathrm{g(9)}\)

• What this tells us: We need to substitute 9 wherever we see x in the function definition

2. TRANSLATE the function evaluation

• \(\mathrm{g(9)}\) means: take the function \(\mathrm{g(x) = x - 12}\) and replace every x with 9
• This gives us: \(\mathrm{g(9) = 9 - 12}\)

3. SIMPLIFY to find the final answer

• Perform the subtraction: \(\mathrm{9 - 12 = -3}\)
• Remember: when subtracting a larger number from a smaller number, the result is negative

Answer: -3 (Choice B)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make an arithmetic error when computing \(\mathrm{9 - 12}\)

Many students struggle with subtraction that results in negative numbers. They might think \(\mathrm{9 - 12 = 3}\) instead of \(\mathrm{-3}\), forgetting that subtracting a larger number from a smaller number gives a negative result.

This may lead them to select Choice C (3)

Second Most Common Error:

Poor TRANSLATE reasoning: Students don't understand what function notation means

Some students see \(\mathrm{g(9)}\) and think it just equals 9, not realizing they need to substitute 9 into the function definition. They might select the input value rather than evaluating the function.

This may lead them to select Choice D (9)

The Bottom Line:

This problem tests whether students understand the fundamental concept of function evaluation through substitution. The arithmetic is straightforward, but the negative result can trip up students who aren't careful with their signs.