The function h is defined by \(\mathrm{h(x) = 3x - 7}\). What is the value of \(\mathrm{h(-2)}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{h(x) = 3x - 7}\)
  • Need to find: \(\mathrm{h(-2)}\)
• This means we need to substitute -2 for x in the function definition

2. SIMPLIFY by substituting and calculating

• Substitute -2 for x: \(\mathrm{h(-2) = 3(-2) - 7}\)
• Calculate the multiplication: \(\mathrm{3(-2) = -6}\)
• Complete the subtraction: \(\mathrm{h(-2) = -6 - 7 = -13}\)

Answer: A. -13

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Sign errors during arithmetic operations

Students might incorrectly calculate \(\mathrm{3(-2)}\) as positive 6 instead of -6, or they might change the subtraction to addition when dealing with negative numbers. For example, calculating \(\mathrm{3(-2) - 7}\) as \(\mathrm{6 + 7 = 13}\).

This may lead them to select Choice D (13).

Second Most Common Error:

Poor TRANSLATE reasoning: Substituting the wrong value

Students might misread -2 as -1 and calculate h(-1) instead. This gives \(\mathrm{h(-1) = 3(-1) - 7 = -3 - 7 = -10}\).

This may lead them to select Choice B (-10).

The Bottom Line:

Function evaluation requires careful attention to both substitution accuracy and sign rules in arithmetic. The negative input value makes this particularly prone to computational errors.