Given:
The given function is [tex]f(x)=\frac{3}{7}(2)^{x}[/tex]
We need to determine the reflection of f(x) over the x - axis
Reflection over x - axis:
The translation rule to reflect over the x - axis is given by
[tex](x, y) \rightarrow(x,-y)[/tex]
Reflecting the function over the x - axis, we get;
[tex]-y=\frac{3}{7}(2)^{x}[/tex]
Multiplying -1 to both sides of the equation, we have;
[tex]y=-\frac{3}{7}(2)^{x}[/tex]
This can be written as
[tex]g(x)=-\frac{3}{7}(2)^{x}[/tex]
Hence, the reflection of the function over the x - axis is [tex]g(x)=-\frac{3}{7}(2)^{x}[/tex]
Thus, Option A is the correct answer.
