Question

identify each function represented with a table of values as: linear, exponential, quadratic, or none of the above.
12.

x	f(x)
1	12
2	18
3	27

______
13.

x	g(x)
1	20
2	10
3	17

______
14.

x	h(x)
1	10
2	22
3	36

______
15.

x	k(x)
1	10
2	15
3	17

______
16.

x	p(x)
1	400
2	200
3	100

______
17.

x	q(x)
1	29
2	31
3	33

______

Explanation:

Step1: Analyze function $f(x)$

Check ratios of consecutive $f(x)$:
$\frac{12}{8}=1.5$, $\frac{18}{12}=1.5$, $\frac{27}{18}=1.5$
Constant ratio means exponential.

Step2: Analyze function $g(x)$

Check first differences:
$20-27=-7$, $10-20=-10$, $17-10=7$
No constant first/second differences or ratio.

Step3: Analyze function $h(x)$

Check second differences:
First differences: $10-0=10$, $22-10=12$, $36-22=14$
Second differences: $12-10=2$, $14-12=2$
Constant second difference means quadratic.

Step4: Analyze function $k(x)$

Check first differences:
$10-7=3$, $15-10=5$, $17-15=2$
No constant first/second differences or ratio.

Step5: Analyze function $p(x)$

Check ratios of consecutive $p(x)$:
$\frac{400}{800}=0.5$, $\frac{200}{400}=0.5$, $\frac{100}{200}=0.5$
Constant ratio means exponential.

Step6: Analyze function $q(x)$

Check first differences:
$29-27=2$, $31-29=2$, $33-31=2$
Constant first difference means linear.

Answer:

1. Exponential
2. None of the above
3. Quadratic
4. None of the above
5. Exponential
6. Linear