# Transformations

• Mar 6th 2011, 03:14 PM
Luna
Transformations
Ok hi

I have a unit test tomorrow regarding transformations and conics. I'm working on some problems on transformations regarding the stretches.

Now, the orig formula (or equation) is y=f(x)

then i have to sketch y=1/2f(1/2x)

what can be done to solve this?

i got y -> 2y and x -> 1/2x this means that i can multiply 2 by y coords on orig points and 1/2 by x coords on orig points to find new points of a transformed drawing? Right?

Thanks
• Mar 6th 2011, 03:28 PM
Luna
Ok I keep getting wrong answers from my current understanding and my understanding isn't matching the answers on the back page, unfortunately. =\
• Mar 6th 2011, 03:51 PM
Soroban
Hello, Luna!

Quote:

The original function is: . $y\,=\,f(x)$

Then i have to sketch: . $y\,=\,\frac{1}{2}f(\frac{1}{2}x)$

The $\frac{1}{2}x$ causes a horizontal dilation.
. . The graph is "twice as wide" (relative to the $y$-axis).

The $\frac{1}{2}f(x)$ causes a vertical contraction.
. . The graph is "half as high" (relative to the $x$-axis).

• Mar 6th 2011, 04:11 PM
Luna
thanks for your response Soroban but the original points are

(0,0), (1,2), (2,0) (3,-2), (4,0) which i found on the graph, so i came up with the transformation (0,0) (0.5, 4), (1, 0), (1.5, -4), and (2,0)
• Mar 6th 2011, 04:15 PM
Luna
from my understanding i have to follow this formula

replacing x with bx (x -> bx) is a horiz stretch about the y axis, y=f(bx) describes a horiz stretch

replacing y with (1/a)y, y -> (1/a)y is a vert stretch about the x axis. i.e. (1/a)y=f(x) or y=af(x) is a vert stretch

a>0 is a vert stretch about x axis by a factor of a

a less than 0 is a vert stretch about the x a xis by a factor of |a| and a reflection in the x axis

b > 0 is a horiz stretch about the y axis by a factor of 1/b

b less than 0 is a horiz stretch bout the y axis a by a factor of 1/|b| and a refle in the y-axis
• Mar 6th 2011, 04:18 PM
Luna
if you want to know, that's the course i'm working on Pure Math 30: Explained!

and i have textbook by me which i copied some of stuff from there to here
• Mar 6th 2011, 04:20 PM
Luna
I hate myself, I wish I could succeed in this.