Error Analysis: A student was asked to decide which table or tables represent a linear function. He incorrectly said that only Table II represents a linear function. Decide which table or tables represent a linear function. What mistake might the student have made?

Question

Error Analysis: A student was asked to decide which table or tables represent a linear function. He incorrectly said that only Table II represents a linear function. Decide which table or tables represent a linear function. What mistake might the student have made?

Table I Table II Table III
Input: 2 | 4 | 6 | 8 | 10 Input: 3 | 6 | 9 | 12| 15 Input: 6 | 3 | 0 | -3 | -6

Output: 8 | 4| 0 | -4 | -8 Output: 9 | 4 | 1 | 0| 1 Output: 219 | 30 | 3 | -24 | -213

Answer 1

The student may have mistaken a linear function for a constant function. In Table II, the output values are increasing by a constant difference of 1 for every increase in the input values, which indicates a linear relationship. However, in Table I and Table III, the output values do not change by a constant difference for each increase in the input values, suggesting a non-linear relationship.

Error Analysis: A student was asked to decide which table or tables represent a linear function. He incorrectly said that only Table II represents a linear function. Decide which table or tables represent a linear function. What mistake might the student have​ made?

Error Analysis: A student was asked to decide which table or tables represent a linear function. He incorrectly said that only Table II represents a linear function. Decide which table or tables represent a linear function. What mistake might the student have made?