If the function h is defined by \(\mathrm{h(n) = \frac{n - 6}{2}}\), what is the value of \(\mathrm{h(4)}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{h(n) = \frac{n - 6}{2}}\)
  • Need to find: \(\mathrm{h(4)}\)
• This tells us we need to substitute \(\mathrm{n = 4}\) into the function

2. SIMPLIFY by substituting and calculating

• Replace n with 4 in the function:
  \(\mathrm{h(4) = \frac{4 - 6}{2}}\)
• Work inside parentheses first:
  \(\mathrm{h(4) = \frac{-2}{2}}\)
• Complete the division:
  \(\mathrm{h(4) = -1}\)

Answer: B. -1

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors, particularly with the subtraction \(\mathrm{4 - 6 = -2}\), or struggle with dividing a negative number by a positive number.

Some students might incorrectly calculate \(\mathrm{(4 - 6)}\) as +2 instead of -2, leading to \(\mathrm{h(4) = \frac{2}{2} = 1}\).
This may lead them to select Choice C (1).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret the function operation and reverse the subtraction order, thinking it should be \(\mathrm{\frac{6 - 4}{2}}\) instead of \(\mathrm{\frac{4 - 6}{2}}\).

This gives them \(\mathrm{h(4) = \frac{6 - 4}{2} = \frac{2}{2} = 1}\), also leading to Choice C (1).

Third Common Error:

Conceptual confusion about function evaluation: Students add instead of subtract, calculating \(\mathrm{\frac{4 + 6}{2} = \frac{10}{2} = 5}\).
This may lead them to select Choice D (5).

The Bottom Line:

This problem tests whether students can accurately substitute into a function and perform basic arithmetic with negative numbers. The key challenges are maintaining the correct order of operations and handling negative values properly.