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
D. She found a nonlinear function instead of a linear function.
Based on the given information, it appears that the student incorrectly concluded that only Table I represents a linear function. The mistake the student might have made is:
D. She found a nonlinear function instead of a linear function
Table III represents a linear function, as it has a constant rate of change.
The student may have made the mistake of choosing Table I as the only table representing a linear function. To identify the mistake, let's examine each answer option:
A. She found the function that decreases instead of increases.
This option suggests that the student may have incorrectly identified a decreasing function as linear. However, none of the tables presented in the question show a consistent decrease in the output values, so this cannot be the mistake.
B. She found the function that represents a straight line.
This option refers to the graphical representation of a linear function. Linear functions are indeed represented by straight lines on a graph, but the question provides tables rather than graphs. Therefore, this option is not applicable in this case.
C. She found the function with a constant rate of change.
A linear function is characterized by a constant rate of change. This means that the difference between consecutive input values will result in the same difference between consecutive output values. If we observe Table I, we can see that the difference between consecutive input values (3, 6, 9, 12, 15) matches the difference between consecutive output values (4, 9, 14, 19, 24). Hence, Table I does have a constant rate of change. However, the student made a mistake as there is another table that also has a constant rate of change.
D. She found a nonlinear function instead of a linear function.
A nonlinear function does not have a constant rate of change and does not represent a straight line on a graph. Since Table I and Table III both have a constant rate of change, the student mistakenly disregarded Table III as representing a linear function. Therefore, this option correctly identifies the mistake made by the student.
So, the mistake the student made is D. She found a nonlinear function instead of a linear function.