The function h is defined by \(\mathrm{h(x) = x + 200}\). What is the value of \(\mathrm{h(50)}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{h(x) = x + 200}\)
  • Need to find: \(\mathrm{h(50)}\)
• What this tells us: We need to substitute \(\mathrm{50}\) for \(\mathrm{x}\) in the function

2. INFER the approach

• To evaluate \(\mathrm{h(50)}\), replace every \(\mathrm{x}\) in the function with \(\mathrm{50}\)
• This gives us: \(\mathrm{h(50) = 50 + 200}\)

3. SIMPLIFY the arithmetic

• Calculate: \(\mathrm{50 + 200 = 250}\)
• Therefore: \(\mathrm{h(50) = 250}\)

Answer: B. 250

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Not understanding what function evaluation means

Students might think \(\mathrm{h(50)}\) involves multiplying the input by the constant, leading them to calculate \(\mathrm{50 \times 200 = 10,000}\) instead of substituting into the expression \(\mathrm{x + 200}\).
This may lead them to select Choice C (10,000)

Second Most Common Error:

Poor TRANSLATE reasoning: Misunderstanding the function notation

Students might think \(\mathrm{h(50)}\) means they should use \(\mathrm{0}\) as the input (focusing on just the "h" part) or get confused about which number goes where, leading them to calculate \(\mathrm{h(0) = 0 + 200 = 200}\).
This may lead them to select Choice A (200)

The Bottom Line:

Function evaluation is about substitution - replace the variable with the given number and then calculate. The key insight is recognizing that \(\mathrm{h(50)}\) means "what does the function output when the input is 50?"