The function f is defined by \(\mathrm{f(x) = -3x + 60}\). What is the value of \(\mathrm{f(x)}\) when x =...

1. INFER what the problem is asking

• We need to find \(\mathrm{f(-8)}\), which means we substitute \(\mathrm{x = -8}\) into our function definition
• Given: \(\mathrm{f(x) = -3x + 60}\)
• Find: \(\mathrm{f(-8)}\)

2. SIMPLIFY by substituting and evaluating

• Replace x with -8 in the function: \(\mathrm{f(-8) = -3(-8) + 60}\)
• Multiply first (order of operations): \(\mathrm{-3(-8) = 24}\)
• Add: \(\mathrm{24 + 60 = 84}\)

Answer: D. 84

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make errors with negative number multiplication or forget order of operations.

Instead of recognizing that \(\mathrm{-3(-8) = 24}\), they might:

• Add instead of multiply: \(\mathrm{-3 + (-8) = -11}\), then \(\mathrm{-11 + 60 = 49}\)
• Ignore the coefficient: \(\mathrm{-8 + 60 = 52}\)
• Ignore the variable: \(\mathrm{-3 + 60 = 57}\)

This leads them to select Choice A (49), Choice B (52), or Choice C (57) instead of the correct answer.

The Bottom Line:

This problem tests careful execution of function substitution. The concept is straightforward, but students must be precise with negative number arithmetic and remember that the coefficient -3 must be multiplied by the entire substituted value (-8).