The function \(\mathrm{G(d) = 16.8 - 0.056d}\) gives the amount of gasoline G, in gallons, remaining in the tank of...

1. TRANSLATE the function notation

• Given: \(\mathrm{G(135) = 9.2}\) where \(\mathrm{G(d) = 16.8 - 0.056d}\)
• In function notation:
  • The value inside parentheses (135) is the input
  • The value after the equals sign (9.2) is the output

2. TRANSLATE each value using context

• The input \(\mathrm{d = 135}\): This represents 135 miles driven since last fill-up
• The output \(\mathrm{G = 9.2}\): This represents 9.2 gallons of gasoline remaining
• Combined meaning: After driving 135 miles, 9.2 gallons remain in the tank

3. INFER which answer choice matches this interpretation

• Looking for: "After 135 miles driven → 9.2 gallons remaining"
• Choice B states exactly this relationship

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students swap the input and output values, thinking \(\mathrm{G(135) = 9.2}\) means "after driving 9.2 miles, 135 gallons remain."

This fundamental confusion about function notation leads them to select Choice C (After being driven for 9.2 miles, the car has 135 gallons of gasoline remaining).

Second Most Common Error:

Poor contextual INFER reasoning: Students recognize the values correctly but misinterpret what \(\mathrm{G(135) = 9.2}\) tells us about the car's behavior, thinking it describes the tank's total capacity or fuel consumption rate rather than remaining fuel at a specific point.

This may lead them to select Choice A (tank capacity) or Choice D (consumption rate).

The Bottom Line:

Function notation problems require students to carefully distinguish between input and output while maintaining awareness of what each variable represents in the real-world context.