The function g is defined by \(\mathrm{g(x) = 4x - 6}\). What is the value of \(\mathrm{g(-7)}\)?

1. TRANSLATE the problem information

• Given information:
  • Function g is defined by \(\mathrm{g(x) = 4x - 6}\)
  • Need to find \(\mathrm{g(-7)}\)
• What this tells us: We need to substitute \(\mathrm{-7}\) for \(\mathrm{x}\) in the function expression

2. TRANSLATE what "g(-7)" means

• \(\mathrm{g(-7)}\) means: replace every \(\mathrm{x}\) in \(\mathrm{g(x) = 4x - 6}\) with \(\mathrm{-7}\)
• This gives us: \(\mathrm{g(-7) = 4(-7) - 6}\)

3. SIMPLIFY the arithmetic

• Calculate \(\mathrm{4(-7)}\): \(\mathrm{4 \times (-7) = -28}\)
• Complete the expression: \(\mathrm{g(-7) = -28 - 6 = -34}\)

Answer: A. -34

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Arithmetic mistakes in the calculation steps

Students might incorrectly calculate:

• \(\mathrm{4(-7) = -22}\) instead of \(\mathrm{-28}\) (forgetting to multiply by 4)
• Or make errors in the final subtraction \(\mathrm{-28 - 6}\)

This may lead them to select Choice B (-22).

Second Most Common Error:

Conceptual confusion about function operations: Working backwards instead of forward

Some students misinterpret the question and try to find the x-value where \(\mathrm{g(x) = -7}\), rather than finding \(\mathrm{g(-7)}\). They solve:

\(\mathrm{4x - 6 = -7}\)
\(\mathrm{4x = -1}\)
\(\mathrm{x = -1/4}\)

This may lead them to select Choice D (-1/4).

The Bottom Line:

This problem tests whether students can correctly apply function notation and perform accurate arithmetic - both fundamental skills that build toward more complex function work.