Answer:
[tex]D.\ (3,\frac{1}{8})[/tex]
Step-by-step explanation:
Given
[tex]y = (\frac{1}{2})^x[/tex]
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:
[tex]D.\ (3,\frac{1}{8})[/tex]
This means that:
[tex]x = 3;\ y = \frac{1}{8}[/tex]
Substitute [tex]x = 3;\ y = \frac{1}{8}[/tex] in [tex]y = (\frac{1}{2})^x[/tex]
[tex]\frac{1}{8} = (\frac{1}{2})^3[/tex]
[tex]\frac{1}{8} = \frac{1^3}{2^3}[/tex]
[tex]\frac{1}{8} = \frac{1}{8}[/tex]
See that the values at the right and left hand side of the equation are the same.
This means that, [tex]D.\ (3,\frac{1}{8})[/tex] lies on [tex]y = (\frac{1}{2})^x[/tex]
