Comparing functions worksheet

Grade 8 math, Common Core 8.F.A.2. 8 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Comparing functions

Grade 8 math, Common Core 8.F.A.2

For each pair, which function has the greater rate of change? Which has the greater initial value?

1.
Function A: y starts at 0 and goes up by 4 for each 1 that x goes up. Function B:
x 0 1 2 3
y 2 8 14 20
2.
Function A: y = 2x + 2. Function B:
x 0 1 2 3
y 6 13 20 27
3.
Function A: y starts at 10 and goes up by 8 for each 1 that x goes up. Function B:
x 0 1 2 3
y 12 18 24 30
4.
Function A: y = x + 3. Function B:
x 0 1 2 3
y 11 15 19 23
5.
Function A: y starts at 5 and goes up by 7 for each 1 that x goes up. Function B:
x 0 1 2 3
y 8 16 24 32
6.
Function A: y = 8x + 12. Function B:
x 1 2 3 4
y 9 12 15 18
7.
Function A: y = 6x + 6. Function B:
x 0 1 2 3
y 12 16 20 24
8.
Function A: y starts at 2 and goes up by 8 for each 1 that x goes up. Function B:
x 0 1 2 3
y 10 17 24 31

x	0	1	2	3
y	2	8	14	20

x	0	1	2	3
y	6	13	20	27

x	0	1	2	3
y	12	18	24	30

x	0	1	2	3
y	11	15	19	23

x	0	1	2	3
y	8	16	24	32

x	1	2	3	4
y	9	12	15	18

x	0	1	2	3
y	12	16	20	24

x	0	1	2	3
y	10	17	24	31

Answer key: Comparing functions

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. Greater rate of change: B (6 vs 4). Greater initial value: B (2 vs 0).
B: y goes up by 6 for each 1 of x, and y = 2 when x = 0
2. Greater rate of change: B (7 vs 2). Greater initial value: B (6 vs 2).
B: y goes up by 7 for each 1 of x, and y = 6 when x = 0
3. Greater rate of change: A (8 vs 6). Greater initial value: B (12 vs 10).
B: y goes up by 6 for each 1 of x, and y = 12 when x = 0
4. Greater rate of change: B (4 vs 1). Greater initial value: B (11 vs 3).
B: y goes up by 4 for each 1 of x, and y = 11 when x = 0
5. Greater rate of change: B (8 vs 7). Greater initial value: B (8 vs 5).
B: y goes up by 8 for each 1 of x, and y = 8 when x = 0
6. Greater rate of change: A (8 vs 3). Greater initial value: A (12 vs 6).
B: y goes up by 3 for each 1 of x; one step back from x = 1 gives y = 9 − 3 = 6
7. Greater rate of change: A (6 vs 4). Greater initial value: B (12 vs 6).
B: y goes up by 4 for each 1 of x, and y = 12 when x = 0
8. Greater rate of change: A (8 vs 7). Greater initial value: B (10 vs 2).
B: y goes up by 7 for each 1 of x, and y = 10 when x = 0

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About comparing functions

Two linear functions can be given in different ways: an equation, a table, a graph or words. To compare them, find each one’s rate of change (slope) and initial value (y when x = 0). The function with the bigger rate of change grows faster.

Worked example 1

Function A: y starts at 3 and goes up by 4 for each 1 that x goes up. Function B:

x	0	1	2	3
y	8	9	10	11

Step 1.B: y goes up by 1 for each 1 of x, and y = 8 when x = 0

Answer: Greater rate of change: A (4 vs 1). Greater initial value: B (8 vs 3).

Watch out for

In a table, the rate of change is the change in y divided by the change in x.
The initial value is the y-value when x = 0. If the table starts at x = 1, work back one step.
Compare like with like: rate with rate, start with start.

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