Effect transformations has on domains?

[ArthurJ]

Hi guys,

Just wondering how transforming the X effects the domain?

if its was y=x^2      -1<x<1
Becomes y= (4x)^2   Whats the new domain?

what about   y= (x/4)^2

Or y=4(x+2) THanks guys!

[arush002]

If the domain -1<x<1 is a restricted domain, given in the question then the transformations shouldn't change the domain.

[brightsky]

nah transformations do have an effect on domains, be they artificially restricted or implied.

if the domain is -1<x<1, and you dilate the graph by a factor of 1/4 from the y-axis, then the domain will become -1/4<x<1/4. but if you dilate from the x-axis, the x-values won't be effected, and so the domain would remain unchanged.

[abeybaby]

it depends very much on how the question is worded. if your questions is:

f has a rule f(x)=x^2, and domain -1<x<1. If the rule is changed to f(x)=(x/4)^2, what is the domain now?
Then the answer is no change. A function is made of a rule and a domain. If you walk around changing the rule, then theres no effect on the domain (since they are specified separately). There will however, be a change IF there is talk of an actual transformation.

f has a rule f(x)=x^2, and domain -1<x<1. f undergoes a dilation by factor 4 from the y-axis. What is the new domain?
Since theres now talk of actual transformation, this applies to the ENTIRETY of the function (rule AND domain). so here, the new domain is -4<x<4. In the previous question, you didnt DO any transformation (you just scribbled out the old rule, and put in a new one), and as such, only the rule was affected. Here, youre affecting the whole function, and so, the domain as well.