If I'm given the graph of
y = sqrt(3x-x^2)
how would I stretch that vertically by 3?
this is not so much a transformation problem. what you have is
or in other words, square both sides and bring the over to get
this is therefore, the upper half of a circle centered at with radius
so now you would know how to stretch it vertically by 3, right? you would have . so the circle looks sort of elliptical. the x-intercepts remain unchanged. but the radius gets distorted vertically
Sorry, but I don't understand.
You say it's not so much a transformation problem, but my book specifically says:
The graph of is given. Use transformations to create a function whose graph is as shown.
Let's say I wanted to get it to shift 2 units to the right (or any other transformation). I don't know how to do that with what I have. In the example you showed, I still don't see what to do to transform it.
Thank you for trying to help thus far.
you should have been more specific as to the question. how exactly would i know that is the nature of the question from your first post?
consider a graph and let be a constant.
then, stretches (vertically) by a factor units
shrinks (vertically) by a factor of
shifts to the left units. ( )
shifts to the right units. ( )
shrinks horizontally by a factor of units. ( )
stretches horizontally by a factor of units, c > 0
reflects in the y-axis
reflects in the x-axis
you should be able to do the transformations you want based on that. so to shift 2 units to the right for example, you want , where , so your new graph is that of
I have another question regarding graph transformations.
How does "absolute value" affect the graph of a function?
My book doesn't directly say anything about it, just gives an example. What I understood from the example is that any part of the graph that's below 0 on the y axis is reflected about it, basically changing it from negative to positive. However, when I was doing a problem, the answer in the back of the book didn't seem to be like that.