\(\mathrm{p(x) = |x - 2|}\)Which table gives three values of x and their corresponding values of p(x) for the given...

1. TRANSLATE the function notation into specific calculations

• Given: \(\mathrm{p(x) = |x - 2|}\)
• Need to find: \(\mathrm{p(1), p(2), and\ p(3)}\)
• This means substituting \(\mathrm{x = 1, x = 2, and\ x = 3}\) into the expression \(\mathrm{|x - 2|}\)

2. SIMPLIFY each calculation step-by-step

For \(\mathrm{p(1)}\):

• \(\mathrm{p(1) = |1 - 2|}\)
• \(\mathrm{= |-1|}\)
• \(\mathrm{= 1}\)

For \(\mathrm{p(2)}\):

• \(\mathrm{p(2) = |2 - 2|}\)
• \(\mathrm{= |0|}\)
• \(\mathrm{= 0}\)

For \(\mathrm{p(3)}\):

• \(\mathrm{p(3) = |3 - 2|}\)
• \(\mathrm{= |1|}\)
• \(\mathrm{= 1}\)

3. INFER which table matches your calculated values

• Looking for the table with: \(\mathrm{(1,1), (2,0), (3,1)}\)
• Table B shows exactly these value pairs

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak conceptual knowledge about absolute value: Students forget that absolute value always produces non-negative results.

They correctly compute \(\mathrm{1 - 2 = -1}\), but then write \(\mathrm{p(1) = -1}\) instead of \(\mathrm{p(1) = |-1| = 1}\). This fundamental misunderstanding of absolute value definition leads them to think negative outputs are possible.

This may lead them to select Choice A \(\mathrm{(-1, 0, 1)}\) since it matches their incorrect calculation for \(\mathrm{p(1)}\).

The Bottom Line:

This problem tests whether students truly understand that absolute value converts any negative result to positive, not just whether they can perform basic substitution and arithmetic.