Answer
Refer to the blue graph below.
Work Step by Step
The parent function of the given function is $y=e^x$.
RECALL:
(i) The graph of $y=f(-x)$ involves a reflection about the $y$ axis of the graph of $y=f(x)$.
(ii) The graph of $y=\dfrac{1}{c} \cdot f(x)$ involves a vertical shrink by a factor of $c$ of the parent function $y=f(x)$.
(iii) The graph of $y=-f(x)$ involves a reflection about the $x$-axis of the parent function $y=f(x)$.
(iv) The graph of $y=f(x)+c$ involves a vertical shift of $c$ units upward of the parent function $y=f(x)$.
The given function is equivalent to $y=-\frac{1}{2}e^{-x}+1$.
This function involves the following transformations of the parent function $y=e^x$:
(1) reflection about the $y$-axis because of the $-x$ exponent;
(2) vertical shrink by a factor of $2$ because of the $\dfrac{1}{2}$ coefficient;
(3) reflection about the $x$-axis because of the $-$ sign before the coefficient; and
(4) a vertical shift of $1$ unit because of the addition of $1$.
Thus, to graph the given function, perform the following steps:
(1) Graph the parent function $y=e^x$ to obtain the black graph below.
(2) Reflect the graph pf $y=e^x$ about the $y$-axis to obtain $y=e^{-x}$ (the green graph below).
(3) Shrink vertically by a factor of $2$ the graph of $y=e^{-x}$ to obtain the graph of $y=\frac{1}{2}e^{-x}$ (the red graph below).
(4) Reflect the graph of $y=\frac{1}{2}e^{-x}$ about the $x$-axis to obtain the graph of $y=-\frac{1}{2}e^{-x}$ (the purple graph below).
(5) Shift the graph of $y=-\frac{1}{2}e^{-x}$ one unit upward to obtain the graph of $y=-\frac{1}{2}e^{-x}+1$ (the blue graph below).
