Silly Questions Thread

[naved_s9994]

What happens when ? ?

I meant it as "". I remember seeing textbooks use the combined , to mean the same thing, so I assumed it is mathematically correct??

Which book, page no?

Thanks!

[m@tty]

I remember reading it, but unfortunately don't remember when or what in Sorry.

[Aqualim]

The curve with equation is transformed under a dilation of factor 4 from the y-axis followed by a translation of 6 units in the negative direction of the x-axis. The equation of the image is:

How is the answer?


Wouldn't it just be;
?

[m@tty]

[Aqualim]

so not matter what equation I'm dilating by 'a' from the y-axis, it will always end up as ?

Therefore when I'm dilating by from the y-axis, it will always end up as 'a'?

[m@tty]

Yep. Sounds right.

Dilation from y-axis by factor of a:

Dilation from y-axis by factor of :

[the.watchman]

so not matter what equation I'm dilating by 'a' from the y-axis, it will always end up as ?

Therefore when I'm dilating by from the y-axis, it will always end up as 'a'?

Failproof way to do this:

When dilation by factor 'k':

- From x-axis: replace y with

- From y-axis: replace x with

So, BECOMES after dilation

[Aqualim]

Thanks

Another terminology question;

Domain of g(f(x))= Domain of f(x)

Would that mean Range of g(f(x)) = Range of g(x)?

[the.watchman]

No, it is the range of g WHEN THE DOMAIN OF F IS APPLIED TO IT!

So if AND

Then Dom gof = Dom f

And for Ran gof, let Dom g = Dom f = R+ U {0}

Then for that domain Ran g = R+ U {0}

So Ran gof = R+ U {0}

Does that make any sense?
I get the feeling it doesn't...

EDIT: lol

[Aqualim]

And for Ran gof, let Dom g = Dom f = R+ U {0}

Then for that domain Ran g = R+ U {0}

So Ran gof = R+ U {0}

Does that make any sense?
I get the feeling it doesn't...

EDIT: lol

Not really, so you have to let the domain of g equal the domain of f?

So if the domain of g was [0,10] and the domain of f was [-15, 25], you would make the domain of g equal [-15,25]? therefore the range of g(f(x)) = [-15,25]?

[GerrySly]

Look at it this way, for the function the domain is but the range you must figure out just like you would any other function.

For example, and



So therefore the domain of is but the range must be worked out from the new function, .



Graphing it you see the range is

[Aqualim]

ok so you'd have to find it by joining the two functions together, and then just sketch it. I thought there just may have been an easier way to work it out. Thank you

[GerrySly]

ok so you'd have to find it by joining the two functions together, and then just sketch it. I thought there just may have been an easier way to work it out. Thank you

Yeah not really a shortcut unless of course it's a straight line then it's just the domain end points. Or if it's not a straight line just get the derivative find the turning point, sub in the domain end points and you'll have 3 y values and just get the highest and lowest values and you'll be sweet

[the.watchman]

Not really, so you have to let the domain of g equal the domain of f?

More or less, sorry about the crappy explanation...

[m@tty]

One 'shortcut' is to let the and then work out on that domain, this range is the range of .