The problem asks to complete a table for the function $y = \frac{1}{2}(7)^x$ for $x = -1, 0, 1, 2$. Then, plot two points to graph the function.

AlgebraExponential FunctionsFunction EvaluationGraphing
2025/6/5

1. Problem Description

The problem asks to complete a table for the function y=12(7)xy = \frac{1}{2}(7)^x for x=1,0,1,2x = -1, 0, 1, 2. Then, plot two points to graph the function.

2. Solution Steps

First, we need to evaluate the function y=12(7)xy = \frac{1}{2}(7)^x for each value of xx.
For x=1x = -1:
y=12(7)1=1217=1140.0714y = \frac{1}{2}(7)^{-1} = \frac{1}{2} \cdot \frac{1}{7} = \frac{1}{14} \approx 0.0714
For x=0x = 0:
y=12(7)0=121=12=0.5y = \frac{1}{2}(7)^{0} = \frac{1}{2} \cdot 1 = \frac{1}{2} = 0.5
For x=1x = 1:
y=12(7)1=127=72=3.5y = \frac{1}{2}(7)^{1} = \frac{1}{2} \cdot 7 = \frac{7}{2} = 3.5
For x=2x = 2:
y=12(7)2=1249=492=24.5y = \frac{1}{2}(7)^{2} = \frac{1}{2} \cdot 49 = \frac{49}{2} = 24.5
To graph the function, we can use the points (0,0.5)(0, 0.5) and (1,3.5)(1, 3.5).

3. Final Answer

The completed table is:
x | y
------- | --------
-1 | 1/14
0 | 1/2
1 | 7/2
2 | 49/2
The points to graph are (0, 0.5) and (1, 3.5).