The function g is defined by the equation \(\mathrm{g(x) = 4x + 7}\). What is the value of \(\mathrm{g(x)}\) when...

1. TRANSLATE the problem information

• Given information:
  • Function definition: \(\mathrm{g(x) = 4x + 7}\)
  • Need to find: \(\mathrm{g(x)}\) when \(\mathrm{x = 5}\)
• This means we need to evaluate \(\mathrm{g(5)}\) by substituting 5 for x in the function

2. SIMPLIFY through substitution and calculation

• Substitute \(\mathrm{x = 5}\) into \(\mathrm{g(x) = 4x + 7}\):
  \(\mathrm{g(5) = 4(5) + 7}\)
• Calculate step by step following order of operations:
  • First: \(\mathrm{4(5) = 20}\)
  • Then: \(\mathrm{20 + 7 = 27}\)

Answer: 27 (Choice D)

Why Students Usually Falter on This Problem

Most Common Error Path:

Incomplete SIMPLIFY execution: Students calculate the first part correctly but forget the constant term.

They compute \(\mathrm{4(5) = 20}\) but forget to add the 7, stopping their calculation early and thinking the answer is just 20.

This may lead them to select Choice B (20)

Second Most Common Error:

Weak TRANSLATE skill: Students misunderstand what "\(\mathrm{g(x)}\) when \(\mathrm{x = 5}\)" means.

They might try to solve \(\mathrm{g(x) = 5}\) instead of evaluating \(\mathrm{g(5)}\), or get confused about how function notation works. This leads to confusion and random guessing among the answer choices.

The Bottom Line:

Function evaluation problems require careful attention to both substitution and complete arithmetic calculation. The most critical step is recognizing that finding "\(\mathrm{g(x)}\) when \(\mathrm{x = 5}\)" simply means plugging 5 into the function definition and calculating the result.