The function g is defined by \(\mathrm{g(x) = 10x + 8}\). What is the value of \(\mathrm{g(x)}\) when x =...

1. TRANSLATE the problem information

• Given information:
  • Function definition: \(\mathrm{g(x) = 10x + 8}\)
  • Need to find: the value of \(\mathrm{g(x)}\) when \(\mathrm{x = 8}\)
• This translates to: Find \(\mathrm{g(8)}\)

2. INFER the solution approach

• To evaluate \(\mathrm{g(8)}\), substitute \(\mathrm{x = 8}\) into the function definition
• Replace every x in \(\mathrm{g(x) = 10x + 8}\) with the value 8

3. SIMPLIFY through substitution and arithmetic

\(\mathrm{g(8) = 10(8) + 8}\)

\(\mathrm{g(8) = 80 + 8}\)

\(\mathrm{g(8) = 88}\)

Answer: D. 88

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may confuse what the question is asking for. Instead of finding \(\mathrm{g(8)}\), they might try to solve for x when \(\mathrm{g(x) = 8}\), leading them to solve \(\mathrm{10x + 8 = 8}\), which gives \(\mathrm{x = 0}\).
This may lead them to select Choice A (0).

Second Most Common Error:

Conceptual confusion about function notation: Students might think that since \(\mathrm{x = 8}\), the answer is just 8, not understanding that they need to substitute this value into the function to get the output.
This may lead them to select Choice B (8).

The Bottom Line:

Function evaluation is straightforward once you understand that you're substituting the input value for x in the function definition. The key is recognizing what the question is asking for and systematically performing the substitution.