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 $y=-f(x)$ involves a reflection about the x-axis of the parent function $f(x)$.
The given function's parent function is $f(x) = x^4$.
The given function can be written as $y=-f(x-1)$.
Thus, the function involves:
(i) a 1-unit shift to the right, and
(ii) a reflection about the x-axis
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) reflect the graph in Step (2) above about the x-axis by changing the y-values to its opposite sign while keeping the values of $x$. (refer to the blue graph in the attached image in the answer part above)
