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: 3 | 6 | 9 | 12 | 15 Input: 4 | 8 | 12 | 16| 20 Input: - 2 | - 4 | - 6 | - 8 | - 10

Output: 8 | -1 | -10 | -19 | -28 Output: 1 | 0 | 1 | 4 9 Output: -21 | -29 | -37 | -45 | -53

Answer 1

The student most likely made the mistake of not recognizing that a linear function has a constant rate of change. In Table II, the output increases by a consistent amount of 1 each time the input increases by 4. However, the other two tables do not have a constant rate of change, indicating that they do not represent linear functions.

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?