The function j is defined by \(\mathrm{j(n) = 4n + 10}\). What is the value of \(\mathrm{j(15)}\)?

1. INFER what the problem is asking

• Given: The function \(\mathrm{j(n) = 4n + 10}\)
• Find: \(\mathrm{j(15)}\)
• This means we need to find the output when the input is 15

2. INFER the approach

• To evaluate \(\mathrm{j(15)}\), substitute \(\mathrm{n = 15}\) into the function definition
• Replace every occurrence of n with 15

3. SIMPLIFY through substitution and calculation

• Start with: \(\mathrm{j(n) = 4n + 10}\)
• Substitute \(\mathrm{n = 15}\): \(\mathrm{j(15) = 4(15) + 10}\)
• Calculate multiplication first: \(\mathrm{j(15) = 60 + 10}\)
• Add: \(\mathrm{j(15) = 70}\)

Answer: 70 (Choice D)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors during calculation

• They might calculate \(\mathrm{4 \times 15 = 50}\) (instead of 60), leading to \(\mathrm{j(15) = 50 + 10 = 60}\)
• Or they might forget to add 10, getting just 60 as their final answer
• This may lead them to select Choice C (60) or Choice B (50)

Second Most Common Error:

Missing conceptual knowledge about function notation: Students don't understand what \(\mathrm{j(15)}\) means

• They might think \(\mathrm{j(15)}\) means "j times 15" instead of "function j evaluated at 15"
• This leads to confusion about what operation to perform
• This causes them to get stuck and guess randomly among the choices

The Bottom Line:

This problem tests whether students understand function notation and can perform careful arithmetic. The key insight is recognizing that function evaluation means substitution, followed by accurate calculation.