Explanation
We have the given function
[tex]f(x)=(\frac{2}{5})^x[/tex]
To determine the behaviour of the function, let us observe the graph
From the graph, we have
[tex]\mathrm{Domain\:of\:}\:\left(\frac{2}{5}\right)^x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:Also[tex]\mathrm{Range\:of\:}\left(\frac{2}{5}\right)^x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(0,\:\infty \:\right)\end{bmatrix}[/tex][tex]\mathrm{Axis\:interception\:points\:of}\:\left(\frac{2}{5}\right)^x:\quad \mathrm{Y\:Intercepts}:\:\left(0,\:1\right)[/tex]
Thus, the answers are
