Error Analysis A student was asked to decide which table or tables represent a linear function.
He incorrectly said that only Table
I represents a linear function. Decide which table or tables represent a linear function. What mistake might the student have made?
Table I
Input
3
6
9
12
15
Output
0
1
4
9
16
Table II
Input
5
10
15
20
25
Output
3
−12
−27
−42
−57
Table III
Input
−3
−6
−9
−12
−15
Output
−23
−35
−47
−59
−71
Question content area bottom
Part 1
Decide which table or tables represent a linear function. Select all that apply.
A.
Table
I
B.
Table
II
C.
Table III
D.
None of the tables represent a linear function.
Error Analysis A student was asked to decide which table or tables represent a linear function.
He incorrectly said that only Table
I represents a linear function. Decide which table or tables represent a linear function. What mistake might the student have made?
Table I
Input
3
6
9
12
15
Output
0
1
4
9
16
Table II
Input
5
10
15
20
25
Output
3
−12
−27
−42
−57
Table III
Input
−3
−6
−9
−12
−15
Output
−23
−35
−47
−59
−71
Question content area bottom
Part 1
Decide which table or tables represent a linear function. Select all that apply.
A.
Table
I
B.
Table
II
C.
Table III
D.
None of the tables represent a linear function.
The student made a mistake by incorrectly stating that only Table I represents a linear function. This is a mistake because both Table II and Table III also represent linear functions. The mistake the student might have made is not properly recognizing the pattern or relationship between the input and output values in Table II and Table III.
table 1:
Input
3 delta x
6 3
9 3
12 3
15 3
Output
0 delta y
1 1
4 3
9 5
16 5 YIKES delta x is constant, 3, but delta y is all over the place so slope m = dy/dx is NOT constant, not a line
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HOWEVER Table 3 seems to have constant slope m = -12/-3 = 4