rational functions (please help me! I need to know how to tell its a stretch or shrink based on the points)

Question

. Explain the transformation of the graph above from the parent function, f(x) = 1/x. Make sure you include an explanation of your thought process. Hint: Check the graph carefully for a stretch or shrink as one of the transformations. (15 points)

Answer 1

so if you make a simple T chart for x & y values, you will see the parent function has

x y

1 1

2 1/2

and if you us the asymptotes shown as the new x/y axis (i.e. shift the origin to where the 2 asymptotes meet) you would get:

x y

1 2

2 1

So you see it is a scale factor of 2 right away (stretch), and now you just need to take care of the translation (when you shifted the origin in the last step); 1 unit to the left (+ with the x) and 2 units up (+ at the end), so

f(x) = (2)(1/(x+1)) +2

I hope this helps!

Answer 2

Given function f(x) = 1/x; then we did horizontal shift by 1 units to the left: we get y = 1/(x + 1)

Then we did vertical stretching by factor 1.8, we get y = 1.8/(x + 1)

And then we did vertical shift by 2 units up, we get g(x)= 1.8/(x + 1) + 2

Answer 3

The graph has been shifted up two units back to the left one unit. If it was a normal graph with just a shift the graph would go through the point ( 0,3 ), it looks like it moved out or got larger so I believe it is a stretch.

Compare it with the graph 1/x compare the shapes.

Good luck