The function f is defined by \(\mathrm{f(x) = 4x - 3}\). What is the value of \(\mathrm{f(10)}\)?

1. TRANSLATE the question

• The problem asks for "the value of f(10)"
• This means: substitute \(\mathrm{x = 10}\) into the function \(\mathrm{f(x) = 4x - 3}\)

2. TRANSLATE the substitution process

• Replace every x in the function with 10
• \(\mathrm{f(10) = 4(10) - 3}\)

3. Calculate the result

• \(\mathrm{f(10) = 4(10) - 3}\)
• \(\mathrm{f(10) = 40 - 3}\)
• \(\mathrm{f(10) = 37}\)

Answer: B. 37

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread or forget part of the function

Many students see \(\mathrm{f(x) = 4x - 3}\) but only use \(\mathrm{f(x) = 4x}\) in their calculations, forgetting the "-3" completely. They calculate \(\mathrm{f(10) = 4(10) = 40}\).

This leads them to select Choice C (40).

Second Most Common Error:

Poor TRANSLATE reasoning: Students flip the sign on the constant term

Some students remember there's a 3 in the function but incorrectly use +3 instead of -3, calculating \(\mathrm{f(10) = 4(10) + 3 = 43}\).

This causes them to select Choice D (43).

The Bottom Line:

Function evaluation problems are deceptively simple - the real challenge lies in accurately reading and preserving every part of the given function during substitution.