Answer:
Option A.
Step-by-step explanation:
Note: The given function should be [tex]f(x)=\dfrac{2}{5}(10)^x[/tex] instead of [tex]f(x)=(10)^x[/tex].
Consider the given function is
[tex]f(x)=\dfrac{2}{5}(10)^x[/tex]
We need to find the function which represents a reflection of f(x) across the x-axis.
If a function f(x) is reflected across the x-axis, then the new function is
[tex]g(x)=-f(x)[/tex]
Using this rule, we get
[tex]g(x)=-\dfrac{2}{5}(10)^x[/tex] [tex][\because f(x)=\dfrac{2}{5}(10)^x][/tex]
Therefore, the correct option is A.
