The function \(\mathrm{C} = \frac{5}{9}(\mathrm{F} - 32)\) gives the temperature in degrees Celsius that is equivalent to a temperature of...

1. TRANSLATE each answer choice into mathematical language

Looking at \(\mathrm{C = (5/9)(F - 32)}\), I need to test what each option means:

• Option A: "C = 32 when F = 0"
• Option B: "F - C = 32 for all temperatures"
• Option C: "C increases by 32 for each 1° increase in F"
• Option D: "F = 32 when C = 0"

2. INFER the testing strategy

• To check these interpretations, I should substitute specific values
• The most revealing test is often when one variable equals zero
• This will show me what the constant 32 actually represents in the function

3. SIMPLIFY by testing each option systematically

Testing Option A: Does C = 32 when F = 0?

\(\mathrm{C = (5/9)(0 - 32)}\)
\(\mathrm{= (5/9)(-32)}\)
\(\mathrm{= -160/9}\)
\(\mathrm{≈ -17.8°C}\)

This doesn't equal 32°C, so Option A is wrong.

Testing Option B: Does F - C = 32 always?

• When F = 32: \(\mathrm{C = (5/9)(32 - 32) = 0}\), so \(\mathrm{F - C = 32 - 0 = 32}\) ✓
• When F = 212: \(\mathrm{C = (5/9)(212 - 32) = 100}\), so \(\mathrm{F - C = 212 - 100 = 112 ≠ 32}\) ✗

The difference isn't constant, so Option B is wrong.

Testing Option C: Does C increase by 32 for each 1° increase in F?

The rate of change is the coefficient of F, which is 5/9, not 32.
So Option C is wrong.

Testing Option D: Does F = 32 when C = 0?

\(\mathrm{0 = (5/9)(F - 32)}\)
Multiply both sides by 9/5: \(\mathrm{0 = F - 32}\)
\(\mathrm{F = 32}\) ✓

Answer: D

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret what the answer choices are claiming and don't convert them into testable mathematical statements.

For example, they might think Option B means "32 is always involved in the calculation" rather than understanding it claims "the numerical difference F - C always equals 32." Without proper translation, they can't systematically test each option and end up guessing.

This leads to confusion and random answer selection.

Second Most Common Error:

Poor INFER reasoning about strategic substitution: Students don't realize that testing when one variable equals zero is the most efficient way to understand what constants mean in functions.

Instead, they might try to work with the function algebraically without strategic substitution, get lost in manipulation, and miss the key insight that setting C = 0 immediately reveals what F equals (which is exactly what Option D describes).

This may lead them to select Choice A (The temperature in Celsius is 32 degrees when the temperature in Fahrenheit is 0 degrees) because they confuse the direction of the relationship.

The Bottom Line:

This problem requires precise interpretation of verbal statements and strategic testing. Success depends on translating each option clearly and choosing smart substitutions to reveal the function's behavior.