The function f is defined by \(\mathrm{f(x) = 80 - 6x}\). What is the value of \(\mathrm{f(7)}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{f(x) = 80 - 6x}\)
  • Need to find: \(\mathrm{f(7)}\)
• What this tells us: We need to substitute \(\mathrm{x = 7}\) into the function

2. TRANSLATE what f(7) means

• \(\mathrm{f(7)}\) means "evaluate the function f when x equals 7"
• This requires substituting 7 everywhere we see x in the function

3. Substitute and SIMPLIFY

• \(\mathrm{f(7) = 80 - 6(7)}\)
• \(\mathrm{f(7) = 80 - 42}\)
• \(\mathrm{f(7) = 38}\)

Answer: B. 38

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Students make order of operations errors when calculating \(\mathrm{80 - 6(7)}\).

Some students might write \(\mathrm{80 - 6 + 7 = 81}\), forgetting that multiplication happens before subtraction. Others might confuse the notation and calculate \(\mathrm{80 - 67 = 13}\), treating "\(\mathrm{6x}\)" as concatenated digits rather than multiplication.

This may lead them to select Choice A (13) or Choice D (81).

Second Most Common Error:

Poor TRANSLATE reasoning: Students substitute the wrong value or make substitution errors.

A student might substitute \(\mathrm{x = 1}\) instead of \(\mathrm{x = 7}\), calculating \(\mathrm{f(1) = 80 - 6(1) = 74}\), possibly due to rushing or misreading the problem.

This may lead them to select Choice C (74).

The Bottom Line:

This problem tests whether students can properly substitute values into functions and follow order of operations. The key is recognizing that \(\mathrm{f(7)}\) means "plug in 7 for x" and then carefully performing the arithmetic.