1. ## Adding a horizontal compression to a graph that is already horizontally compressed?

I need to add a horizontal compression by a factor of 1/4, then a reflection in the y-axis, followed by 2 units down.

Original equation is y = 3x - 6

I understand how to do expansions, compressions, translations, etc, but I don't understand how to add a horizontal compression of 1/4 when the original equation already shows a horizontal compression of 1/3. Do I multiply them together to get a horizontal compression of 1/12?

I am also wondering what would happen if the original equation was y = 1/3x - 6. How do I add a horizontal compression to an equation that already has a horizontal expansion?

Thanks very much for any help.

2. ## Re: Adding a horizontal compression to a graph that is already horizontally compresse

Originally Posted by mint12
Original equation is y = 3x - 6

I understand how to do expansions, compressions, translations, etc, but I don't understand how to add a horizontal compression of 1/4 when the original equation already shows a horizontal compression of 1/3.
You can start with any function $f(x)$. Then the graph of $g(x)=f(kx)$ is obtained from the graph of $f(x)$ by horizontal compression with factor $k$. By this I mean that every point of the graph of $y = g(x)$ is $k$ times closer to the $Oy$ axis than the corresponding point of the graph of $y = f(x)$.

3. ## Re: Adding a horizontal compression to a graph that is already horizontally compresse

sorry I didn't understand well, I'm still new to this. are you able to tell me just what alterations I can make to the equation itself when adding a compression or expansion onto another compression or expansion? or is that not possible?

4. ## Re: Adding a horizontal compression to a graph that is already horizontally compresse

This problem does not involve adding compression onto another compression. It has a single compression applied to y = 3x - 6. I don't understand why you are considering this function as the result of another compression. To squeeze the graph of f(x) k times around the Oy axes, replace x in f(x) with kx.

5. ## Re: Adding a horizontal compression to a graph that is already horizontally compresse

I only learned every equation starts with y=f(x) and then making those changes like kx means compressing or expanding it. I haven't learned beyond that so I don't know how to add a compression to anything that isn't the base equation. I still don't understand even what "oy axes" is so I'll just look for help elsewhere. Thanks for your responses