Quick Q (1 Viewer)

[_trickster_]

hey BoS, just wonderin if theres any way to find out the Range of a function quickly
without graphing it
like, is there a formula or something?

 

[Timothy.Siu]

yeah sure, i'll give you the formula.
do you need a formula for life as well?

 

[lychnobity]

hey BoS, just wonderin if theres any way to find out the Range of a function quickly
without graphing it
like, is there a formula or something?

No.

The only "quick" way is to sit there and figure it out using logic. ie

Step 1: Figure out what it can't equal to
Step 2: Figure out where the graph exists
Step 3: Write this down.

 

[madsam]

step 4: graph it (just to be sure)

 

[Michaelmoo]

I guess its just a technique you develop when you look at a lot of graphs. Some common techniques to determine the range:

1) An exponential within a function always has a range of y>0
2) Take a limit of x--> +-infinity. Although, this does not always restrict the range as the graph can cross a horizonal asymptote
3) Functions in the form of f(x)/q(x) usually have a restricted range. e.g. the rectangular hyperbola
4) Any quadratic has a restricted range.

But thats only some of them. Like I said, you just learn this stuff when you do a lot of graphs. Otherwise, sketching is the best option you have.

 

[blaze.bluetane]

yeah sure, i'll give you the formula.
do you need a formula for life as well?

lol.
yes it is about intuition, substituting values and seeing where it exists
1. denominator of fraction can never be 0 [well for the purpose of domain/range]
2. you cannot substitute any negative value into a log naturale function
3. Even powers may have limited range, while odd can usually exist everywhere
4. the exponential function is always greater than 0

5. Look at limits (approaching infinity and negative infinity and approaching limiting values)---from the + and - side

good luck

oh and make sure you know the domain and range of trig functions (and inverse trig)

 

[kaz1]

Look at the allowable y values.

 

[_trickster_]

sweet cheers guys