The function g is defined by \(\mathrm{g(x) = \frac{240}{x}}\). What is the value of \(\mathrm{g(12)}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{g(x) = \frac{240}{x}}\)
  • Need to find: \(\mathrm{g(12)}\)
• What this tells us: We need to substitute \(\mathrm{x = 12}\) into the function

2. SIMPLIFY by substitution and calculation

• Substitute \(\mathrm{x = 12}\) into \(\mathrm{g(x) = \frac{240}{x}}\):
  \(\mathrm{g(12) = \frac{240}{12}}\)
• Calculate the division:
  \(\mathrm{240 \div 12 = 20}\)

Answer: B (20)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skills: Students misunderstand what \(\mathrm{g(12)}\) means and perform the wrong operation with the numbers 240 and 12.

Instead of substituting \(\mathrm{x = 12}\) into the function, they might:

• Add: \(\mathrm{240 + 12 = 252}\)
• Subtract: \(\mathrm{240 - 12 = 228}\)

This may lead them to select Choice D (252) or Choice C (228).

Second Most Common Error:

Poor SIMPLIFY execution: Students understand they need to calculate \(\mathrm{\frac{240}{12}}\) but make an arithmetic error in the division.

Common calculation mistakes include confusing the division process or rushing through the arithmetic, leading them to arrive at 12 instead of 20.

This may lead them to select Choice A (12).

The Bottom Line:

This problem tests whether students truly understand function notation - that \(\mathrm{g(12)}\) means "substitute 12 for x in the function" rather than "do something with 12 and 240." The arithmetic itself is straightforward once the substitution concept is clear.