Question 822022
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:
{{{y= 2x-13/x-5}}}
which is not a transformation from y = 1/x. What you meant must have been
{{{y= (2x-13)/(x-5)}}}
which should be posted as:
y= (2x-13)/(x-5)<br>
For part a we will start by using long division to divide:
<pre>
               2
        __________
x - 5  / 2x - 13
         2x - 10
        --------
              -3
</pre>So now we have:
{{{y = 2 + (-3)/(x-5)}}}
Now we'll move some things around to make the transformations more obvious:
{{{y = (-3)/(x-5) + 2}}}
{{{y = (-3)*(1/(x-5)) + 2}}}
Let f(x) = 1/x. Then we can write:
{{{y = (-3)*(f(x-5)) + 2}}}<br>
Part b. The transformations:<ul><li>The f(x-5) indicates a phase/horizontal shift/translation to the right by 5 units.</li><li>The +2 indicates a vertical shift/translation of up 2 units.</li><li>The minus of -3 indicates a reflection across the horizontal axis (which has been moved up to y = 2 by the vertical shift).</li><li>The 3 of -3 indicates a vertical stretching by a factor of 3.</li></ul>Here's what the graphs look like (your function in red, f(x) = 1/x in green):
{{{graph(600, 600, -3, 9, -4, 8, 2+(-3)/(x-5), 1/x)}}}<br>
I'll leave the other function for you to do.