在下方坐标系中画出 $y = 3^{-x}$ 的图像草图。 清晰地标出图像与坐标轴交点的坐标。

1. Find the intercepts with the axes.

For the $y$-axis intercept, put $x=0$:
$y=3^{-0}=3^0=1.$
So the graph crosses the $y$-axis at $(0,1)$.

For the $x$-axis intercept, put $y=0$:
$3^{-x}=0.$
But $3^{-x}>0$ for all real $x$, so there is no $x$-axis intercept.

2. Sketch the decreasing exponential curve with correct asymptotic behaviour.

Since
$y=3^{-x}=\left(\frac{1}{3}\right)^x,$
the graph is a decreasing exponential curve. It stays above the $x$-axis and approaches $y=0$ as $x$ increases.