The function f is defined by \(\mathrm{f(x) = x^3 + 9}\). What is the value of \(\mathrm{f(2)}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{f(x) = x^3 + 9}\)
  • Need to find: \(\mathrm{f(2)}\)
• This means substitute \(\mathrm{x = 2}\) into the function

2. SIMPLIFY through substitution and calculation

• Substitute 2 for x: \(\mathrm{f(2) = (2)^3 + 9}\)
• Compute the exponent: \(\mathrm{2^3 = 2 \times 2 \times 2 = 8}\)
• Add: \(\mathrm{f(2) = 8 + 9 = 17}\)

Answer: C. 17

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak conceptual knowledge of exponents: Students may not correctly compute \(\mathrm{2^3}\), instead treating it as \(\mathrm{2 \times 3 = 6}\), leading to \(\mathrm{f(2) = 6 + 9 = 15}\).

This may lead them to select Choice B (15).

Second Most Common Error:

Poor SIMPLIFY execution: Students may confuse the base and exponent, computing \(\mathrm{3^2 = 9}\) instead of \(\mathrm{2^3 = 8}\), leading to \(\mathrm{f(2) = 9 + 9 = 18}\).

This may lead them to select Choice D (18).

The Bottom Line:

This problem tests basic function evaluation skills, but students often struggle with exponent computation or make simple arithmetic errors under pressure.