Question

1. identify if the following tables are linear functions or exponential functions.

7.

x	-3	-2	-1	0	1	2
y	8	4	2	1	0.5	0.25

8.

x	1	2	3	4	5	6
y	2	0	-2	-4	-6	-8

9.

x	1	2	3	4	5	6
y	-8	-5	-2	1	4	7

10.

x	-1	0	1	2	3
y	3	\\(\frac{3}{2}\\)	\\(\frac{3}{4}\\)	\\(\frac{3}{8}\\)	\\(\frac{3}{16}\\)

Explanation:

(for Table 7):

Step1: Check x - differences

x values: -3, -2, -1, 0, 1, 2. Differences: $(-2)-(-3)=1$, $(-1)-(-2)=1$, $0 - (-1)=1$, $1 - 0 = 1$, $2 - 1 = 1$. Constant (1).

Step2: Check y - differences

y values: 8, 4, 2, 1, 0.5, 0.25. Differences: $4 - 8=-4$, $2 - 4=-2$, $1 - 2=-1$, $0.5 - 1=-0.5$, $0.25 - 0.5=-0.25$. Not constant.

Step3: Check y - ratios

Ratios: $\frac{4}{8}=0.5$, $\frac{2}{4}=0.5$, $\frac{1}{2}=0.5$, $\frac{0.5}{1}=0.5$, $\frac{0.25}{0.5}=0.5$. Constant (0.5). So exponential.

(for Table 8):

Step1: Check x - differences

x: 1,2,3,4,5,6. Differences: $2 - 1 = 1$, $3 - 2 = 1$, etc. Constant (1).

Step2: Check y - differences

y: 2,0,-2,-4,-6,-8. Differences: $0 - 2=-2$, $-2 - 0=-2$, etc. Constant (-2). So linear.

(for Table 9):

Step1: Check x - differences

x:1,2,3,4,5,6. Differences: $2 - 1 = 1$, etc. Constant (1).

Step2: Check y - differences

y: -8,-5,-2,1,4,7. Differences: $-5 - (-8)=3$, $-2 - (-5)=3$, etc. Constant (3). So linear.

(for Table 10):

Step1: Check x - differences

x: -1,0,1,2,3. Differences: $0 - (-1)=1$, $1 - 0 = 1$, etc. Constant (1).

Step2: Check y - differences

y: 3, $\frac{3}{2}$, $\frac{3}{4}$, $\frac{3}{8}$, $\frac{3}{16}$. Differences: $\frac{3}{2}-3=-\frac{3}{2}$, $\frac{3}{4}-\frac{3}{2}=-\frac{3}{4}$, not constant.

Step3: Check y - ratios

Ratios: $\frac{\frac{3}{2}}{3}=\frac{1}{2}$, $\frac{\frac{3}{4}}{\frac{3}{2}}=\frac{1}{2}$, etc. Constant ($\frac{1}{2}$). So exponential.

Answer:

• Table 7: Exponential Function
• Table 8: Linear Function
• Table 9: Linear Function
• Table 10: Exponential Function