Answer
Refer to the image below for the graph.
The graph of $h(x)$ is red, the graph of the parent function is blue.
Work Step by Step
RECALL:
The graph of the function $g(x) = a^x + k$ involves a vertical shift of $|k|$ units of the parent function $f(x) = a^x$. The shift is upward when $k$ is positive and downward then $k$ is negative.
The given function $h(x) = 4+(\frac{1}{2})^x$ has its parent function $f(x) = (\frac{1}{2})^x$.
The given function has $k=4$ so it involves a 4-unit upward shift of the graph of its parent function.
Thus, to graph the given function, perform the following steps:
(1) Graph the parent function $f(x) = (\frac{1}{2})^x$ by creating a table of values then connecting the points using a smooth curve.
(refer to the attached table below, the graph is attached in the answer part above)
(2) Draw the graph of $h(x)$by moving the graph of the parent function 4 units upward. The graph of $h(x)$ is red, the graph of the parent function is blue.
(refer to the attached image in the answer part above for the graph)
