To determine which function represents the reflection of [tex]\( f(x) = 2(0.35)^x \)[/tex] over the [tex]\( y \)[/tex]-axis, you need to understand how reflections work in the coordinate plane.
A reflection of a function [tex]\( f(x) \)[/tex] over the [tex]\( y \)[/tex]-axis is achieved by replacing [tex]\( x \)[/tex] with [tex]\( -x \)[/tex] in the function [tex]\( f(x) \)[/tex].
Given the original function:
[tex]\[ f(x) = 2(0.35)^x \][/tex]
To reflect this function over the [tex]\( y \)[/tex]-axis, we replace [tex]\( x \)[/tex] with [tex]\( -x \)[/tex]:
[tex]\[ h(x) = 2(0.35)^{-x} \][/tex]
Thus, the function [tex]\( h(x) \)[/tex] that represents the reflection of [tex]\( f(x) \)[/tex] over the [tex]\( y \)[/tex]-axis is:
[tex]\[ h(x) = 2(0.35)^{-x} \][/tex]
Among the given options, this corresponds to:
[tex]\[ h(x) = 2(0.35)^{-x} \][/tex]
Therefore, the answer is:
[tex]\[ h(x) = 2(0.35)^{-x} \][/tex]
The correct option is:
[tex]\[ h(x) = 2(0.35)^{-x} \][/tex]
