Question 1091976
<br>I haven't seen the idea of transformations applied to the parent function 1/x; but the ideas are the same, and they work nicely.<br>
We need to get the given function<br>
{{{(4x-15)/(x-3)}}}<br>
in the form<br>
{{{a(1/(x-b))+c}}}<br>
When we have the function in that form, b will be the horizontal shift, a will be the vertical stretch (including a reflection in the x axis, if a is negative), and c will be the vertical shift.<br>
{{{(4x-15)/(x-3) = (4x-12)/(x-3) - 3/(x-3) = 4 - 3/(x-3) = -3(1/(x-3))+4}}}<br>
So the given function, compared to the parent function 1/x, has a horizontal shift 3 to the right, a vertical stretch of -3 (stretched by 3 and reflected over the x axis), and a vertical shift of 4.<br>
You should now be able to fill in the blanks in the question as you show it.