The graph of y equals root of order three of three minus x end root plus one is shown below. what are the x-intercept and the y-intercept, and what is the location of the inflection point?

We have that

y=∛(3-x) + 1

using a graph tool
see the attached figure

the x intercept is the value of x when y=0
the x intercept is the point (4,0)

the y intercept is the value of y when x=0
the y intercept is the point (0,2.442)

the inflection point is where a curve changes from Concave upward to Concave downward (or vice versa)

the inflection point is the point (3,1)