The function f is defined by the equation \(\mathrm{f(x) = 100x + 2}\). What is the value of \(\mathrm{f(x)}\) when...

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{f(x) = 100x + 2}\)
  • Need to find: \(\mathrm{f(x)}\) when \(\mathrm{x = 9}\)
• This means we need to substitute 9 for every x in the function

2. SIMPLIFY by substituting and calculating

• Substitute \(\mathrm{x = 9}\) into \(\mathrm{f(x) = 100x + 2}\):

\(\mathrm{f(9) = 100(9) + 2}\)

• Calculate step by step:
  • First: \(\mathrm{100 \times 9 = 900}\)
  • Then: \(\mathrm{900 + 2 = 902}\)

Answer: D. 902

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students correctly substitute but make arithmetic errors or forget parts of the calculation.

The most frequent mistake is calculating \(\mathrm{100(9) = 900}\) but then forgetting to add the \(\mathrm{+2}\), stopping at 900. This leads them to select Choice C (900).

Second Most Common Error:

Incomplete TRANSLATE reasoning: Students might misunderstand what "f(x) when x = 9" means, potentially trying to solve \(\mathrm{100x + 2 = 9}\) instead of substituting 9 for x.

This confusion about the basic meaning of function evaluation can cause them to get stuck and guess randomly among the answer choices.

The Bottom Line:

This problem tests the fundamental skill of function evaluation. While conceptually straightforward, students often stumble on the execution - either through careless arithmetic or by misunderstanding what the question is asking them to do.