Which graph represents a reflection of f(x) = 2(0.4)x across the y-axis?

The correct option is A.

Explanation:

The given function is,

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 . Since , so the given function is decreasing function.

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,

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.