Math worksheet for identifying linear, exponential, and quadratic functions from tables.
Worksheet titled "Comparing Linear, Exponential, and Quadratic Functions" with ten tables showing x and y values for identifying function types.
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Step-by-step solution for: Comparing Linear, Exponential, and Quadratic Functions Worksheets ...
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Show Answer Key & Explanations
Step-by-step solution for: Comparing Linear, Exponential, and Quadratic Functions Worksheets ...
Let’s go through each table one by one to figure out if it’s linear, exponential, or quadratic.
We’ll look at how the y-values change as x increases.
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- Linear: The *difference* between consecutive y-values is constant (same amount added/subtracted each time).
- Exponential: The *ratio* between consecutive y-values is constant (multiply by same number each time).
- Quadratic: The *second differences* are constant (differences of the differences are the same).
---
## Problem 1:
x: 2, 4, 6, 8, 10
y: 12, 0, -4, 0, 12
First, find first differences (change in y):
0 - 12 = -12
-4 - 0 = -4
0 - (-4) = +4
12 - 0 = +12
Differences: -12, -4, +4, +12 → Not constant → not linear.
Now second differences:
(-4) - (-12) = +8
(+4) - (-4) = +8
(+12) - (+4) = +8
Second differences are constant (+8) → Quadratic
✔ Answer: Quadratic
---
## Problem 2:
x: -2, -1, 0, 1, 2
y: 1, 2, 4, 8, 16
Check ratios:
2 ÷ 1 = 2
4 ÷ 2 = 2
8 ÷ 4 = 2
16 ÷ 8 = 2
Constant ratio → Exponential
✔ Answer: Exponential
---
## Problem 3:
x: -3, -2, -1, 0, 1
y: 11, 8, 5, 2, -1
First differences:
8 - 11 = -3
5 - 8 = -3
2 - 5 = -3
-1 - 2 = -3
Constant difference → Linear
✔ Answer: Linear
---
## Problem 4:
x: -2, -1, 0, 1, 2
y: -2, 1, 4, 7, 10
First differences:
1 - (-2) = +3
4 - 1 = +3
7 - 4 = +3
10 - 7 = +3
Constant difference → Linear
✔ Answer: Linear
---
## Problem 5:
x: -2, -1, 0, 1, 2
y: -6, -6, -4, 0, 6
First differences:
-6 - (-6) = 0
-4 - (-6) = +2
0 - (-4) = +4
6 - 0 = +6
Differences: 0, 2, 4, 6 → Not constant → not linear.
Second differences:
2 - 0 = +2
4 - 2 = +2
6 - 4 = +2
Constant second differences → Quadratic
✔ Answer: Quadratic
---
## Problem 6:
x: -2, -1, 0, 1
y: 0.08, 0.4, 2, 10
Check ratios:
0.4 ÷ 0.08 = 5
2 ÷ 0.4 = 5
10 ÷ 2 = 5
Constant ratio → Exponential
✔ Answer: Exponential
---
## Problem 7:
x: 0, 1, 2, 3, 4
y: 3, 2, 3, 6, 11
First differences:
2 - 3 = -1
3 - 2 = +1
6 - 3 = +3
11 - 6 = +5
Differences: -1, 1, 3, 5 → Not constant.
Second differences:
1 - (-1) = +2
3 - 1 = +2
5 - 3 = +2
Constant second differences → Quadratic
✔ Answer: Quadratic
---
## Problem 8:
x: -3, -2, -1, 0, 1
y: 4, 0, -2, -2, 0
First differences:
0 - 4 = -4
-2 - 0 = -2
-2 - (-2) = 0
0 - (-2) = +2
Differences: -4, -2, 0, 2 → Not constant.
Second differences:
(-2) - (-4) = +2
0 - (-2) = +2
2 - 0 = +2
Constant second differences → Quadratic
✔ Answer: Quadratic
---
## Problem 9:
x: 0, 2, 1, -1, -2 ← Wait! These x-values are NOT in order. Let’s reorder them from smallest to largest:
Reorder x: -2, -1, 0, 1, 2
Corresponding y: 0.5, 1, 2, 4, 8
So now:
x: -2, -1, 0, 1, 2
y: 0.5, 1, 2, 4, 8
Check ratios:
1 ÷ 0.5 = 2
2 ÷ 1 = 2
4 ÷ 2 = 2
8 ÷ 4 = 2
Constant ratio → Exponential
✔ Answer: Exponential
---
## Problem 10:
x: 0, 2, 4, -2, -4 ← Again, not in order. Reorder:
x: -4, -2, 0, 2, 4
y: -5, -2, 1, 4, 7
First differences:
-2 - (-5) = +3
1 - (-2) = +3
4 - 1 = +3
7 - 4 = +3
Constant difference → Linear
✔ Answer: Linear
---
Final Answer:
1. Quadratic
2. Exponential
3. Linear
4. Linear
5. Quadratic
6. Exponential
7. Quadratic
8. Quadratic
9. Exponential
10. Linear
We’ll look at how the y-values change as x increases.
---
🔢 Quick Rules:
- Linear: The *difference* between consecutive y-values is constant (same amount added/subtracted each time).
- Exponential: The *ratio* between consecutive y-values is constant (multiply by same number each time).
- Quadratic: The *second differences* are constant (differences of the differences are the same).
---
## Problem 1:
x: 2, 4, 6, 8, 10
y: 12, 0, -4, 0, 12
First, find first differences (change in y):
0 - 12 = -12
-4 - 0 = -4
0 - (-4) = +4
12 - 0 = +12
Differences: -12, -4, +4, +12 → Not constant → not linear.
Now second differences:
(-4) - (-12) = +8
(+4) - (-4) = +8
(+12) - (+4) = +8
Second differences are constant (+8) → Quadratic
✔ Answer: Quadratic
---
## Problem 2:
x: -2, -1, 0, 1, 2
y: 1, 2, 4, 8, 16
Check ratios:
2 ÷ 1 = 2
4 ÷ 2 = 2
8 ÷ 4 = 2
16 ÷ 8 = 2
Constant ratio → Exponential
✔ Answer: Exponential
---
## Problem 3:
x: -3, -2, -1, 0, 1
y: 11, 8, 5, 2, -1
First differences:
8 - 11 = -3
5 - 8 = -3
2 - 5 = -3
-1 - 2 = -3
Constant difference → Linear
✔ Answer: Linear
---
## Problem 4:
x: -2, -1, 0, 1, 2
y: -2, 1, 4, 7, 10
First differences:
1 - (-2) = +3
4 - 1 = +3
7 - 4 = +3
10 - 7 = +3
Constant difference → Linear
✔ Answer: Linear
---
## Problem 5:
x: -2, -1, 0, 1, 2
y: -6, -6, -4, 0, 6
First differences:
-6 - (-6) = 0
-4 - (-6) = +2
0 - (-4) = +4
6 - 0 = +6
Differences: 0, 2, 4, 6 → Not constant → not linear.
Second differences:
2 - 0 = +2
4 - 2 = +2
6 - 4 = +2
Constant second differences → Quadratic
✔ Answer: Quadratic
---
## Problem 6:
x: -2, -1, 0, 1
y: 0.08, 0.4, 2, 10
Check ratios:
0.4 ÷ 0.08 = 5
2 ÷ 0.4 = 5
10 ÷ 2 = 5
Constant ratio → Exponential
✔ Answer: Exponential
---
## Problem 7:
x: 0, 1, 2, 3, 4
y: 3, 2, 3, 6, 11
First differences:
2 - 3 = -1
3 - 2 = +1
6 - 3 = +3
11 - 6 = +5
Differences: -1, 1, 3, 5 → Not constant.
Second differences:
1 - (-1) = +2
3 - 1 = +2
5 - 3 = +2
Constant second differences → Quadratic
✔ Answer: Quadratic
---
## Problem 8:
x: -3, -2, -1, 0, 1
y: 4, 0, -2, -2, 0
First differences:
0 - 4 = -4
-2 - 0 = -2
-2 - (-2) = 0
0 - (-2) = +2
Differences: -4, -2, 0, 2 → Not constant.
Second differences:
(-2) - (-4) = +2
0 - (-2) = +2
2 - 0 = +2
Constant second differences → Quadratic
✔ Answer: Quadratic
---
## Problem 9:
x: 0, 2, 1, -1, -2 ← Wait! These x-values are NOT in order. Let’s reorder them from smallest to largest:
Reorder x: -2, -1, 0, 1, 2
Corresponding y: 0.5, 1, 2, 4, 8
So now:
x: -2, -1, 0, 1, 2
y: 0.5, 1, 2, 4, 8
Check ratios:
1 ÷ 0.5 = 2
2 ÷ 1 = 2
4 ÷ 2 = 2
8 ÷ 4 = 2
Constant ratio → Exponential
✔ Answer: Exponential
---
## Problem 10:
x: 0, 2, 4, -2, -4 ← Again, not in order. Reorder:
x: -4, -2, 0, 2, 4
y: -5, -2, 1, 4, 7
First differences:
-2 - (-5) = +3
1 - (-2) = +3
4 - 1 = +3
7 - 4 = +3
Constant difference → Linear
✔ Answer: Linear
---
Final Answer:
1. Quadratic
2. Exponential
3. Linear
4. Linear
5. Quadratic
6. Exponential
7. Quadratic
8. Quadratic
9. Exponential
10. Linear
Parent Tip: Review the logic above to help your child master the concept of identify linear quadratic and exponential functions from tables worksheet.
