The function g is defined by the equation \(\mathrm{g(x) = 5x - 6}\). What is the value of \(\mathrm{g(x)}\) when...

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{g(x) = 5x - 6}\)
  • Need to find: "the value of g(x) when x = 3"
• What this tells us: We need to find \(\mathrm{g(3)}\)

2. INFER the solution approach

• To evaluate \(\mathrm{g(3)}\), substitute \(\mathrm{x = 3}\) into the function definition
• Replace every x in \(\mathrm{g(x) = 5x - 6}\) with the value 3

3. SIMPLIFY through calculation

\(\mathrm{g(3) = 5(3) - 6}\)

\(\mathrm{g(3) = 15 - 6}\)

\(\mathrm{g(3) = 9}\)

Answer: C) 9

Why Students Usually Falter on This Problem

Most Common Error Path:

Sign confusion: Students may incorrectly change the subtraction to addition when performing calculations.

Instead of \(\mathrm{g(3) = 5(3) - 6 = 15 - 6 = 9}\), they calculate \(\mathrm{g(3) = 5(3) + 6 = 15 + 6 = 21}\).

This may lead them to select Choice E (21).

Second Most Common Error:

Operation confusion: Students may use addition instead of multiplication in the function.

Instead of recognizing that \(\mathrm{5x}\) means 5 times x, they treat it as \(\mathrm{5 + x}\), calculating \(\mathrm{g(3) = 5 + 3 - 6 = 2}\).

This may lead them to select Choice A (2).

The Bottom Line:

This problem tests careful attention to mathematical notation and basic arithmetic accuracy. Success requires precise translation of function notation and systematic execution of the substitution process.