1 answer:
Answer:
![D.\ (3,\frac{1}{8})](https://tex.z-dn.net/?f=D.%5C%20%283%2C%5Cfrac%7B1%7D%7B8%7D%29)
Step-by-step explanation:
Given
![y = (\frac{1}{2})^x](https://tex.z-dn.net/?f=y%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%29%5Ex)
Required
Points that lies on the above graph
From the given options, only option D lies on the point and the proof is as follows:
![D.\ (3,\frac{1}{8})](https://tex.z-dn.net/?f=D.%5C%20%283%2C%5Cfrac%7B1%7D%7B8%7D%29)
This means that:
![x = 3;\ y = \frac{1}{8}](https://tex.z-dn.net/?f=x%20%3D%203%3B%5C%20y%20%3D%20%5Cfrac%7B1%7D%7B8%7D)
Substitute
in ![y = (\frac{1}{2})^x](https://tex.z-dn.net/?f=y%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%29%5Ex)
![\frac{1}{8} = (\frac{1}{2})^3](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E3)
![\frac{1}{8} = \frac{1^3}{2^3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D%20%3D%20%5Cfrac%7B1%5E3%7D%7B2%5E3%7D)
![\frac{1}{8} = \frac{1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D%20%3D%20%5Cfrac%7B1%7D%7B8%7D)
See that the values at the right and left hand side of the equation are the same.
This means that,
lies on ![y = (\frac{1}{2})^x](https://tex.z-dn.net/?f=y%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%29%5Ex)
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