The function f is defined by \(\mathrm{f(x) = 3x - 8}\). What is the value of \(\mathrm{f(7)}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{f(x) = 3x - 8}\)
  • Need to find: \(\mathrm{f(7)}\)

• What this tells us: We need to substitute \(\mathrm{x = 7}\) into the function expression

2. TRANSLATE what "f(7)" means

• \(\mathrm{f(7)}\) means "evaluate the function f when \(\mathrm{x = 7}\)"
• This requires substituting 7 everywhere we see x in the function expression
• So \(\mathrm{f(7) = 3(7) - 8}\)

3. SIMPLIFY the expression

\(\mathrm{f(7) = 3(7) - 8}\)

\(\mathrm{f(7) = 21 - 8}\)

\(\mathrm{f(7) = 13}\)

Answer: B. 13

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misreading the function equation as \(\mathrm{f(x) = 3x + 8}\) instead of \(\mathrm{f(x) = 3x - 8}\)

Students might rush through reading and miss that it's subtraction, not addition. When they substitute \(\mathrm{x = 7}\), they calculate \(\mathrm{f(7) = 3(7) + 8 = 21 + 8 = 29}\).

This leads them to select Choice A (29).

Second Most Common Error:

Poor TRANSLATE reasoning: Confusing the input value and substituting the wrong number

Students might misread \(\mathrm{f(7)}\) as \(\mathrm{f(1)}\) or accidentally think about \(\mathrm{f(-7)}\). For example:

• If they calculate \(\mathrm{f(1)}\): \(\mathrm{f(1) = 3(1) - 8 = 3 - 8 = -5}\)
• If they calculate \(\mathrm{f(-7)}\): \(\mathrm{f(-7) = 3(-7) - 8 = -21 - 8 = -29}\)

This may lead them to select Choice C (-5) or Choice D (-29).

The Bottom Line:

This problem tests careful reading and basic function evaluation. The arithmetic is straightforward once you correctly identify what needs to be substituted where.