\(\mathrm{g(x) = 11x + 4}\). For the given linear function g, which table shows three values of x and their...

1. TRANSLATE the problem requirements

• Given information:
  • Function: \(\mathrm{g(x) = 11x + 4}\)
  • Need to find which table shows correct \(\mathrm{g(x)}\) values for \(\mathrm{x = -1, 0,}\) and \(\mathrm{1}\)
• What this tells us: We need to evaluate the function at these three specific x-values

2. INFER the solution strategy

• To determine the correct table, calculate \(\mathrm{g(x)}\) for each x-value
• Compare our calculated results to what each table shows
• The matching table will be our answer

3. SIMPLIFY by evaluating the function at each x-value

For \(\mathrm{x = -1}\):

\(\mathrm{g(-1) = 11(-1) + 4}\)

\(\mathrm{= -11 + 4}\)

\(\mathrm{= -7}\)

For \(\mathrm{x = 0}\):

\(\mathrm{g(0) = 11(0) + 4}\)

\(\mathrm{= 0 + 4}\)

\(\mathrm{= 4}\)

For \(\mathrm{x = 1}\):

\(\mathrm{g(1) = 11(1) + 4}\)

\(\mathrm{= 11 + 4}\)

\(\mathrm{= 15}\)

4. Compare results to the tables

Our calculations show: \(\mathrm{(-1, -7), (0, 4), (1, 15)}\)

Checking each choice:

• Choice A shows \(\mathrm{(-1, 7)}\) but we got \(\mathrm{(-1, -7)}\) ❌
• Choice B shows \(\mathrm{(-1, -4)}\) but we got \(\mathrm{(-1, -7)}\) ❌
• Choice C shows \(\mathrm{(-1, -7), (0, 4), (1, 15)}\) - perfect match! ✅
• Choice D shows \(\mathrm{(-1, -11)}\) but we got \(\mathrm{(-1, -7)}\) ❌

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Sign errors when working with negative numbers

When calculating \(\mathrm{g(-1) = 11(-1) + 4}\), students often make one of these mistakes:

• Calculate \(\mathrm{11(-1) = 11}\) instead of \(\mathrm{-11}\) (forgetting negative times positive = negative)
• Get confused about \(\mathrm{-11 + 4}\) and calculate \(\mathrm{-15}\) instead of \(\mathrm{-7}\)

This leads them to select Choice A (which shows \(\mathrm{g(-1) = 7}\)) if they calculated \(\mathrm{11(-1) + 4 = 11 + 4 = 15}\), then confused the sign.

Second Most Common Error:

Incomplete SIMPLIFY process: Forgetting to add the constant term

Students correctly calculate the \(\mathrm{11x}\) part but forget to add 4:

• \(\mathrm{g(-1) = 11(-1) = -11}\) (forgetting the \(\mathrm{+4}\))
• \(\mathrm{g(0) = 11(0) = 0}\) (forgetting the \(\mathrm{+4}\))
• \(\mathrm{g(1) = 11(1) = 11}\) (forgetting the \(\mathrm{+4}\))

This may lead them to select Choice D which shows these "incomplete" values.

The Bottom Line:

This problem tests careful arithmetic execution more than conceptual understanding. The strategy is straightforward, but students must be methodical with signs and remember all parts of the function formula.