When a function is reflected, it must be reflected over a line.
The function that represents a reflection over the x-axis is: [tex]\mathbf{g(x) = -\frac{3}{7}(2)^x}[/tex]
The function is given as:
[tex]\mathbf{f(x) = \frac{3}{7}(2)^x}[/tex]
The rule of reflection over the x-axis is:
[tex]\mathbf{(x,y) \to (x,-y)}[/tex]
So, we have:
[tex]\mathbf{g(x) = -f(x)}[/tex]
This gives:
[tex]\mathbf{g(x) = -\frac{3}{7}(2)^x}[/tex]
Hence, the function that represents a reflection over the x-axis is: [tex]\mathbf{g(x) = -\frac{3}{7}(2)^x}[/tex]
Read more about reflections at:
https://brainly.com/question/938117
