Answer
a. III
b. I
c. II
d. IV
Work Step by Step
a. $f(x) = 2^x$
$2^x$ has a point (1,2); the only graph that matches with that is in red (III)
b. $f(x) = 2^{-x}$
This is a graph that is reflected over the y-axis from $2^x$, thus it is the graph in green (I)
c. $f(x) = (-2)^x$
This is a graph that is reflected over the x-axis from $2^x$, thus it is the graph in purple (II)
d. $f(x) = (-2)^{-x}$
This is a graph that is reflected over the x and y-axis from $2^x$, thus it is the graph in black (IV)
