1) Note that this question refers to a transformation of the function 1/x
2) Looking attentively, we can see that the plus 10 is outside of the x term. So this implies that this is a vertical shift as we can see here:
3) Thus, the answer is Shift 10 units up
a) As we can see there are some points in which this function is not defined.
In the denominator, x cannot be equal to zero. Besides that, the function is defined for all Real Set. So we can tell the Domain is:
Note that 0 is not included.
b) Range
Looking at the graph, we can see that for y=10 there is an asymptote so we cannot include 10 on the Range Set. And as there is no other undefined point for that function we can write that the Range is defined according to this rule:
c) We can look for the Monotone Intervals in this function. As we can see, in the following intervals the function is decreasing:
f'(x) = -1/x², f'(x)<0
So there are no intervals in which this function is increasing.
The decreasing intervals are:
[tex]-\infty \: