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# C1 Transformation help watch

1. I just want to find out examples of graph transformations for stretches of graphs. I wrote down in my notes a sort of way to answer similar transformation questions. I wrote "y=af(x) stretches y=f(x) by a scale factor of a parallel to the y-axis" and "y=f(ax) stretches y=f(x) by a scale factor of 1/a to the x axis"

But when doing some past papers I wasn't able to indicate which one it would be. What graphs would follow the formula y=af(x) and y=f(x)
2. (Original post by Fruitbasket786)
I just want to find out examples of graph transformations for stretches of graphs. I wrote down in my notes a sort of way to answer similar transformation questions. I wrote "y=af(x) stretches y=f(x) by a scale factor of a parallel to the y-axis" and "y=f(ax) stretches y=f(x) by a scale factor of 1/a to the x axis"

But when doing some past papers I wasn't able to indicate which one it would be. What graphs would follow the formula y=af(x) and y=f(x)
Your notes are absolutely correct

For example, take the graph y=x^2 (squared).
To stretch this graph parallel to the y axis, you want to stretch the y coordinates of the graph, which is after you've squared the x values. Therefore to stretch with scale factor 4 would be y=4(x^2) as you take an x value, square it (which gives you the corresponding y value) and then multiply this by 4 to get the y stretch.
To stretch this graph parallel to the x axis, you want to stretch the x coordinates, which is before you've squared them to get the corresponding y values. Therefore to stretch with scale factor 4 would be y=1/4x^2 (no brackets needed due to BIDMAS rules). Sorry if this isn't too clear, it's hard to type value like that, it reads a quarter x squared.

Take another graph: y=7x-22.
To stretch in the y direction, s.f. 5 for example -> y=5(7x-22) as you need to stretch the y values which are the x values after they are put into the function.
To strecth in the x direction, s.f. 5 for example -> y=(5*7)x-22, therefore y=35x-22 as you want to stretch the x values.

Hope that made some form of sense and I didn't just confuse you more! The more practice you do of these, the easier it will become. Just think that stretching parallel to the y axis means the y values are altered and parallel to the x axis means the x values are altered. Y values are found from the 'output' of the function whereas x values are the 'input'.
3. I kind of see what you're trying to say, but I thinking about what the letter "a" could be when it comes to graphs and my equation.
4. (Original post by Fruitbasket786)
I kind of see what you're trying to say, but I thinking about what the letter "a" could be when it comes to graphs and my equation.
The letter a is the scale factor, therefore substitute a in for where I've used 4 and 5. It's likely in the exam you'll be given actual numbers (at least this tends to happen on my exam board, I do OCR).
5. I do OCR aswell, but I'm really confused with the the difference in the placement of a which is the scale factor. I just don't see the difference in the general translation formula with y=af(x) y=f(ax). Would y=af(x) be something like y=8x^3 and y=f(ax) be something like y=2x.
6. (Original post by Fruitbasket786)
I do OCR aswell, but I'm really confused with the the difference in the placement of a which is the scale factor. I just don't see the difference in the general translation formula with y=af(x) y=f(ax). Would y=af(x) be something like y=8x^3 and y=f(ax) be something like y=2x.
y=a(fx) means that you put the scale factor, a, outside of a bracket with the main function inside, e.g. y=4x^2 + 19x + 4 => y=a(4x^2 + 19x + 4). Think of it as being y=a(f(x)) where a is a constant which multiplies the whole function.
y=f(ax) means that you put the scale factor, a, before the x value only, e.g. y=24x - 19 => y=24ax - 19. You can see the -19 remains unaffected.

The example you gave with y=8x^3 would be y=af(x) since x^3 is the function, then you multiply the whole function by 8 to get y=8x^3.
The example with y=2x could either be a stretch scale factor 2 in the y direction or a stretch scale factor 1/2 in the x direction, here they are equivalent. Something that is y=f(ax) could follow the pattern y=ax^2 + ax + c, where the c is not affected by the a.
7. Alright, I get it now. Thanks alot for helping me out!
8. Also good luck on the Exam tomorrow!
9. (Original post by Fruitbasket786)
Also good luck on the Exam tomorrow!
You too

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