Answer
Refer to the blue graph below.
Work Step by Step
The parent function of $y= -2^{-x}$ is $y=2^x$.
Recall:
(i) The graph of $y=f(-x)$ involves a reflection about the $y$-axis of the parent function $y=f(x)$.
(ii) The graph of $y=-f(x)$ invlolves a reflection about the $x$-axis of the parent function $y=f(x)$.
Note that the function $y=-2^{-x}$ involves the following transformations of the parent function $y=2^x$:
(1) reflection about the $y$-axis because of the exponent $-x$.; and
(2) reflection about the $x$-axis because of the $-$ sign outside $f(x)$.
Thus, to graph the given function, perform the following steps:
(1) Graph $y=2^x$ (refer to the black graph below).
(2) Reflect the graph of $y=2^x$ about the $y$-axis to obtain the graph of $y=2^{-x}$ (refer to the green graph below).
(3) Reflect the graph of $y=2^{-x}$ about the $x$-axis to obtain the graph of $y=-2^{-x}$ (refer to the blue graph below).
