The correct option is A.
The given function is,
f(x) = 2(0.4)^xTo find the graph of this function after the reflecting across y-axis, first we have to find the graph of the equation.
The value of the function is 2 when x=0, so, the graph of given equation intersect the y-axis at 2.
In the equation (0.4)^x. Since 0 < 0.4 < 1. , so the given function is decreasing function.
f(x) → 0 as → ∞
f(x) → ∞ as → -∞
The value of f(x) is always positive, so the graph of f(x) is always above the x-axis. Thus, the graph must be above the x-axis after reflection across y-axis.
So, the option (2) and (4) and incorrect.
When we reflect the graph across the y-axis then,
f(x) → ∞ as → ∞
f(x) → 0 as → -∞
It means when x approaches to large negative number the f(x) approaches to 0 and when x approaches to large positive number the f(x) approaches to infinite.
Therefore, the correct option is show in first graph.