Answer
Refer to the blue graph below.
Work Step by Step
The parent function of the given function is $y=e^x$.
The given function is equivalent to: $y=2(-e^x+1)$.
RECALL:
(i) The graph of $y=-f(x)$ involves a reflection about he $x$-axis of the parent function $y=f(x)$.
(ii) The graph of the function $y=f(x)+c$ involves a vertical shift of $c$ units upward of the parent function $y=f(x)$.
(iii) The graph of $c\cdot f(x)$ involves a vertical stretch by a factor of $c$ of the parent function $y=f(x)$.
The function $y=2(-e^x+1)$ involves the following transformations of the parent function $y=e^x$:
(1) a reflection about the $x$-axis;
(2) a vertical shift of $1$ unit upward; and
(3) a vertical stretch by a factor of $2$.
Thus, to graph the given function, perform the following steps:
(1) Graph the parent function $y=e^x$ (refer to the black graph below).
(2) Reflect the graph of $y=e^x$ about the $x$-axis to obtain the graph of $y=-e^{x}$ (refer to the green graph below).
(3) Shift the graph of $y=e^{-x}$ one unit upward to obtain the graph of $y=-e^{x}+1$ (refer to the red graph below).
(4) Stretch vertically by a factor of $2$ the graph of $y=-e^x+1$ to obtain the graph of $y=2(-e^x+1)$.
