First of all, please put parentheses around numerators and denominators, especially if they are not just a positive integer or variable. What you posted meant:
which is not a transformation from y = 1/x. What you meant must have been
which should be posted as:
y= (2x-13)/(x-5)
For part a we will start by using long division to divide:
2
__________
x - 5 / 2x - 13
2x - 10
--------
-3
So now we have:
Now we'll move some things around to make the transformations more obvious:
Let f(x) = 1/x. Then we can write:
Part b. The transformations:- The f(x-5) indicates a phase/horizontal shift/translation to the right by 5 units.
- The +2 indicates a vertical shift/translation of up 2 units.
- The minus of -3 indicates a reflection across the horizontal axis (which has been moved up to y = 2 by the vertical shift).
- The 3 of -3 indicates a vertical stretching by a factor of 3.
Here's what the graphs look like (your function in red, f(x) = 1/x in green):
I'll leave the other function for you to do.