The function g is defined by \(\mathrm{g(t) = \frac{6t + 7}{5}}\). What is the value of \(\mathrm{g(8)}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{g(t) = \frac{6t + 7}{5}}\)
  • Need to find: \(\mathrm{g(8)}\)
• What this tells us: We need to substitute \(\mathrm{t = 8}\) into the function definition

2. SIMPLIFY through systematic substitution

• Substitute \(\mathrm{t = 8}\): \(\mathrm{g(8) = \frac{6(8) + 7}{5}}\)
• Work through the numerator first (order of operations):
  • Multiply: \(\mathrm{6 \times 8 = 48}\)
  • Add: \(\mathrm{48 + 7 = 55}\)
• Now we have: \(\mathrm{g(8) = \frac{55}{5}}\)
• Perform final division: \(\mathrm{55 \div 5 = 11}\)

Answer: C) 11

Why Students Usually Falter on This Problem

Most Common Error Path:

Incomplete SIMPLIFY execution: Students correctly substitute and calculate the numerator (6(8) + 7 = 55), but forget to complete the division by 5.

They see \(\mathrm{g(8) = \frac{6(8) + 7}{5}}\) = \(\mathrm{\frac{48 + 7}{5}}\) = \(\mathrm{\frac{55}{5}}\), but stop at "55" without performing the final division step.

This leads them to select Choice E (55).

Second Most Common Error:

Poor SIMPLIFY organization: Students make arithmetic errors while working through multiple calculation steps, such as incorrectly calculating \(\mathrm{6 \times 8}\) or making addition/division mistakes.

These calculation errors can produce various incorrect results, causing them to select wrong answer choices or become confused and guess.

The Bottom Line:

Function evaluation problems require careful, systematic calculation through multiple arithmetic steps. The key is recognizing that finding \(\mathrm{g(8)}\) means complete substitution followed by thorough simplification—don't stop until you've worked through every operation in the expression.