Answer
Refer to the blue graph below.
Work Step by Step
RECALL:
(1) The function $y=f(x-h)$ involves either a horizontal shift of $h$ units to the right of the parent function $f(x)$ if $h \gt0$, or a horizontal shift of $|h|$ units to the left when $h\lt0$.
(2) The function $y=f(x)+k$ involves either a vertical shift of $k$ units upward of the parent function $f(x)$ when $k\gt0$, or a vertical shift of $|k|$ units downward when $k\lt0$.
The given function's parent function is $f(x) = x^4$.
The given function can be written as $y=f(x-1)+2$.
Thus, the function involves:
(i) a 1-unit shift to the right, and
(ii) a 2-unit shift upward
of the parent function $f(x)$
To graph the given function, perform the following steps:
(1) Graph the parent function $f(x) = x^4$. (refer to the red graph below).
(2) Shift the graph of the parent function 1 unit to the right. (refer to the green graph below)
(3) shift the graph in Step (2) above 2 units upward by adding 2 to each of the y-values while keeping the values of $x$. (refer to the blue graph in the attached image in the answer part above)
