a
We're looking for the #y#-intercept - which means that #x=0#:
#h(x)=3+abs(x-2)#
#h(0)=3+abs(0-2)#
#h(0)=3+abs(-2)#
#h(0)=3+2=5#
b
The range is the list of #y# values associated with a domain. Let's find the highest value first.
By the graph, the range is at the maximum at #h(7)#:
#h(7)=3+abs(7-2)#
#h(7)=3+5=8#
To find the minimum value, we first need to know at what #x# value it occurs. We can do that by observing that the absolute value function will only return positive values - the smallest value it can return is 0. So where will #abs(x-2)=0#? At #x=2#.
#:. h(2)=3+abs(2-2)#
#h(2)=3#
#:. "Range": 3<=h(x)<=8#