Question

identifying tables
given a table of values in which there is a constant change in x-values, the pattern in the y-values identifies the type of function.
linear

x	y
0	-8
3	-6
6	-7
9	-8
12	-8

there is a common first difference in y-values.
quadratic

x	y
-2	-0
-1	5
0	9
1	9
2	5

there is a common second difference in y-values.
exponential

x	y
1	2
1	6
2	18
3	54
4	162

there is a common ratio in y-values.
classify each table of values as linear, quadratic, exponential growth, exponential decay, or none of the above.
19.

x	-10	-6	-2	2
y	-4	-6	-8	-10

20.

x	-2	-1	0	1
y	135	45	15	5

21.

x	0	2	4	6
y	-5	25	59	97

22.

x	1	4	7	10
y	3	12	48	192

23.

x	-5	0	5	10
y	-16	-9	-2	5

24.

x	3	4	5	6
y	14	26	44	68

Explanation:

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Table 19

Step1: Check x-value increment

$(-6)-(-10)=4$, $(-2)-(-6)=4$, $2-(-2)=4$ (common increment of 4)

Step2: Check 1st y-differences

$(-6)-(-4)=-2$, $(-8)-(-6)=-2$, $(-10)-(-8)=-2$ (common first difference)
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Table 20

Step1: Check x-value increment

$(-1)-(-2)=1$, $0-(-1)=1$, $1-0=1$ (common increment of 1)

Step2: Check y-value ratios

$\frac{45}{135}=\frac{1}{3}$, $\frac{15}{45}=\frac{1}{3}$, $\frac{5}{15}=\frac{1}{3}$ (common ratio <1)
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Table 21

Step1: Check x-value increment

$2-0=2$, $4-2=2$, $6-4=2$ (common increment of 2)

Step2: Check 1st y-differences

$25-(-5)=30$, $59-25=34$, $97-59=38$ (no common 1st difference)

Step3: Check 2nd y-differences

$34-30=4$, $38-34=4$ (common second difference)
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Table 22

Step1: Check x-value increment

$4-1=3$, $7-4=3$, $10-7=3$ (common increment of 3)

Step2: Check y-value ratios

$\frac{12}{3}=4$, $\frac{48}{12}=4$, $\frac{192}{48}=4$ (common ratio >1)
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Table 23

Step1: Check x-value increment

$0-(-5)=5$, $5-0=5$, $10-5=5$ (common increment of 5)

Step2: Check 1st y-differences

$(-9)-(-16)=7$, $(-2)-(-9)=7$, $5-(-2)=7$ (common first difference)
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Table 24

Step1: Check x-value increment

$4-3=1$, $5-4=1$, $6-5=1$ (common increment of 1)

Step2: Check 1st y-differences

$26-14=12$, $44-26=18$, $68-44=24$ (no common 1st difference)

Step3: Check 2nd y-differences

$18-12=6$, $24-18=6$ (common second difference)
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Answer:

1. Linear
2. Exponential decay
3. Quadratic
4. Exponential growth
5. Linear
6. Quadratic