I can't remember them so should I make a poster or something? Any help is appreciated Thanks!
How to remember Transformations of Functions (GCSE)? watch
- Thread Starter
- 12-04-2016 18:04
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- Community Assistant
- Study Helper
- 12-04-2016 18:12
f(x) + a
The constant is outside the brackets so these all occur in the y-direction i.e. up and down.
The constant is inside the brackets so these are all in the x-direction i.e. left and right. And for these it's good to remember that the direction/scale factor is "opposite". I.e. f(2x) is a strech by 1/2 and f(x + 2) is a translation 2 to the left even though +2 seems to suggest 2 to the right.
f(x - 3)
The constant is inside the brackets so this is going to be a left-to-right transformation. And I recognise it as a translation. -3 would "usually" mean 3 to the left but the constant is inside the brackets so we do the opposite. So this is a translation 3 units to the right.
Let me know if you need more help.Last edited by Notnek; 12-04-2016 at 18:16.
- Thread Starter
- 12-04-2016 18:14
That should help for now, thanks!
- 12-04-2016 18:16
Idk, I try to understand them instead of memorising them because everything seems to stick a lot better.
- 12-04-2016 19:01
- 12-04-2016 20:22
In my approach, we look at what happens to the *axes* (represented by the letters ), not what happens to the function. It is a more consistent way to look at transformations.
Suppose that then we have:
Note that we have rearranged the second equation to indicate how the axis variable is changed. Both the x- and y-axes are now treated the same way (they are both additions)
In both these cases, we have added to the axis variable. We interpret this as moving the *axis* units in the +ve direction, while holding the function in place. This now makes sense: a +ve shift always moves something in +ve direction (and that thing is the axis). This now works consistently both for the and axes.
Since the axis has moved in the +ve direction, it looks like the function has moved in the -ve direction, but we no longer think of it like that: remember: a +ve shift always moves the axis +ve.
For -ve shifts, we apply the same reasoning, but now the axis moves -ve while the function is held in place; again we treat the axis variable consistently:
Again, note that a -ve number *always* corresponds to a -ve shift (of the axes).
b) Scale factors
Again the second equation now looks like the first, as far as the axis variable goes. We can now interpret both in the same way. And for scaling, we interpret this as saying that we have stretched the *axis* by a factor of while keeping the function unchanged. To look at a specific example, we may have:
where both indicate that the axis has been stretched by a factor of 2, making it look like the function was shrunk by a factor 1/2 relative to the now-larger axis; because we now treat the x- and y- axes consistently, we don't have to remember different rules for "inside and outside the brackets". Similarly with:
we see that the axis has been shrunk by 2, while keeping the function unchanged. Consequently, the function seems to have been stretched by a factor of 2.