Let’s look at each table one by one and check how the y-values change as x increases by 1.
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First Table:
x | y
--|--
1 | 5
2 | 9
3 | 13
4 | 17
5 | 21
Check the differences between consecutive y-values:
9 - 5 =
4
13 - 9 =
4
17 - 13 =
4
21 - 17 =
4
→ The difference is always 4. That means it’s
linear.
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Second Table:
x | y
--|--
1 | 0
2 | -1
3 | 0
4 | 3
5 | 8
First differences (change in y):
-1 - 0 =
-1
0 - (-1) =
+1
3 - 0 =
+3
8 - 3 =
+5
Not constant → not linear.
Now check second differences (differences of the first differences):
+1 - (-1) =
2
+3 - (+1) =
2
+5 - (+3) =
2
→ Second differences are constant (all 2). That means it’s
quadratic.
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Third Table:
x | y
--|--
1 | 3
2 | 9
3 | 27
4 | 81
5 | 243
Check ratios (divide each y by the previous y):
9 ÷ 3 =
3
27 ÷ 9 =
3
81 ÷ 27 =
3
243 ÷ 81 =
3
→ Each time, we multiply by 3. That means it’s
exponential.
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Final Answer:
The first table is linear, the second is quadratic, and the third is exponential.
Parent Tip: Review the logic above to help your child master the concept of identify linear quadratic and exponential functions from tables worksheet.
