Translations before dilations?

[wildareal]

What's the effect of translations before dilations as opposed to dilations before translations? I know you're always told to do dilations first and then translations, but I heard that there are questions we're translations are first and then dilations. What would the effect be on a sin or cos graph? Cheers

[kyzoo]

Sometimes the question will specifically state to translate before dilation, however if there is not specified, then it will always be dilation then translation.

The effect of mixing up the order is different resultant graphs despite the same original graph. Try it out yourself with some sample functions.

[crappy]

Remember, DR T, this is the order.

say it out aloud, "Doctor T"

[kyzoo]

Arghhh I just hate mnemonics ^. They don't help with understanding the concept or logic at all, they are so artificial, so arbitrary.

[stonecold]

the only confusing part for me is when you have to go from a graph that already has transformations applied to it, back to the original graph.

do you go backwards for this. i.e. translations, then reflections, then dilations.

for example a question might be state the transformations that transform the graph of  to

Would it be correct to say:
-translate 1 unit in the positive direction of the y-axis
-translate 3 units in the positive direction of the x-axis
-reflect in the x-axis
-dilate by factor 1/2 from x-axis

is this correct?

[m@tty]

Try replacing 'x'  and 'y' with your stated transformations.





Translate 1 unit up, 3 units right.
Sub and




Reflect in x-axis, dilate by factor of from x axis.
Sub





As this is the required rule, yes these transformations will work. All these dashes are gay.  :buck2:

[stonecold]

oooh i like that.  you can sort of check your answer hehe.

i remember there is some pain question the the essential book where you have to go backwards.
definitely going to try and do it again, because last time i managed to screw it up big time!

[Gloamglozer]

Remember, DR T, this is the order.

say it out aloud, "Doctor T"

Or you could remember it by knowing the alphabetical order.    lol

[m@tty]

oooh i like that.  you can sort of check your answer hehe.

i remember there is some pain question the the essential book where you have to go backwards.
definitely going to try and do it again, because last time i managed to screw it up big time!

Try using the above method for your original question, except in the 'normal' order, DR T, you will see it does not produce the same result. When going 'backwards' you generally go reverse order, T DR.

[jimmy999]

When asked to list the order of transformations of one function to the other, it is generally easier to follow the order of DRT.
However be aware that you can go in any order you want, it's just the scale factor of each transformation will be different in order to obtain the same result.