Answer: The correct option is A.
Explanation:
The given function is,
[tex]f(x)=2(0.4)^x[/tex]
To 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 [tex](0.4)^x[/tex]. Since [tex]0<0.4<1[/tex], so the given function is decreasing function.
[tex]f(x)\rightarrow 0 \text{ as }\rightarrow \infty[/tex]
[tex]f(x)\rightarrow \infty \text{ as }\rightarrow -\infty[/tex]
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,
[tex]f(x)\rightarrow \infty \text{ as }\rightarrow \infty[/tex]
[tex]f(x)\rightarrow 0 \text{ as }\rightarrow -\infty[/tex]
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.
