Error Analysis A student was asked to decide which table or tables represent a linear function. She incorrectly said that only Table I represents a linear function. Decide which table or tables represent a linear function. What meccake me the stiutend have made?
Table 1 Table Il 5 10 15 20 25 Input 3 6 9 12 15 Output 3-367-77 Output 4 9 Input 16 28 Table III 8-10 Input -2 4-6 Output-24-32-40-48-56
Decide which table or tables represent a linear function. Table III Table |
What mistake might the student have made?
A. She found the function that decreases instead of increases. B. She found the function that represents a straight line. C. She found the function with a constant rate of change D. She found a nonlinear function instead of a linear function
The student made mistake A. She found the function that decreases instead of increases.
The mistake the student might have made is option D. She found a nonlinear function instead of a linear function.
To decide which table or tables represent a linear function, we need to examine the patterns in the input and output values. A linear function is characterized by a constant rate of change, meaning that as the input value increases by a certain amount, the output value also increases by a consistent amount.
Looking at Table I:
Input: 5, 10, 15, 20, 25
Output: 3, 6, 9, 12, 15
We can observe that as the input value increases by 5, the output value increases by 3. This constant increase indicates a linear relationship.
Next, let's analyze Table II:
Input: 3, 6, 9, 12, 15
Output: 3, -3, 6, -7, -77
In this table, the output values do not increase or decrease consistently as the input values increase. The pattern here is not linear.
Finally, let's examine Table III:
Input: -2, 4, -6
Output: -24, -32, -40, -48, -56
Similar to Table II, the output values in Table III do not exhibit a constant increase or decrease as the input values change. Therefore, it is not a linear function.
Considering the analysis, the student made a mistake by incorrectly choosing Table I as the only representation of a linear function. The correct choice would be C. She found the function with a constant rate of change.