How to find DOMAIN AND RANGE for a function (KristaKingMath)

► My Precalculus course: www.kristakingmath.com/precal...
The domain of a function is the full set of values for which the independent variable (usually x) is defined. The range of a function is the full set of values that will be returned to you if you plug in every value from the domain.
Therefore, when you're looking for the domain and range of a function, you want to find the domain first, and then use any limitations from the domain to find the range.
When you're working on the domain, instead of trying to find all of the values that are included, look for all of the values that should be excluded. For example, values of x that would make an expression underneath a square root negative, or values that would make a denominator zero. These are values that should be excluded from the domain, and the exclusion of the values will of course effect the range as well.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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[@Dune0312]

Krista! I love the sound of your voice!!! it is so soothing and so gentle! Love your explanations also, very easy to understand what your are saying. I thank you so much for your videos!

[@jayceinfinitealgharhythmns9814]

Even though this is precalculus... it was a brilliant idea to start with the basics first! Great job, Thanks!

[@syamalchattopadhyay2893]

Outstanding clarity in the video lecture.

[@kristakingmath]

I appreciate it!

[@allanlule8094]

Thanks for reminding me about basics of a functions and more

[@Dune0312]

Krista I love your voice.

[@rohanvekaria9574]

any tip on how remember all ur math rules... i tend to forget stuff after sometime if i am not using them and then i gotta re-learn them thanks!

[@kristakingmath]

+rohan vekaria Like you said, it's use it or lose it. But I'd collect all of the formulas and rules in one place, and then seeing them all together over and over might help you remember them better.

[@EM-du6ch]

thank you so much

[@kristakingmath]

You're welcome! Glad I could help!

[@MrAyangan]

Can you please explain what happens to the range of a many-one function (I'm using this term to mean functions which have same values of f(x) for different x such as sin(x), I'm not sure what their actual name is) where the function is undefined at any one point but defined at others for example take the function f(x)=((x^2)*(x-2))/(x-2). Can you please help me I can't figure out how to express the range of this function.

[@3RuLe5]

great!!!

[@kristakingmath]

Chanuka Chathuranga thanks!

[@3RuLe5]

:)

[@pakmath1103]

If f and g are differentiable functions of one variable, prove that integration over closed smooth curve C (f(x)dx+g(y)dy)=0 for every piecewise-smooth simple closed curve in D. Green's Theorem problem. plz send me its solution.

[@offtheball87]

The range of this function should be all real numbers, shouldn't it? At the upper limits of the domain, 10^2x will apprach 10^14, but ln(21 - 3x) will approach negative infinity. It'll be positive until you get very close to 7, but it will go negative, and it will go all the way. For the negative side, 10^2x approaches 0 as ln(21 - 3x) approaches infinity, so the function approaches infinity.

[@parneetkaur1996]

There is one negative value as well in range (-3.51) How can u say that all are positive ????????????

[@jameskeyser5124]

just wanted to thank you this accelerated calc stuff is rough

[@kristakingmath]

Accelerated calc is SUPER tough, hang in there! I hope the videos are helping. :)

[@AmirHameed-picwellwisher12pk]

you are so cute :)

[@thomassutter9073]

This is incorrect. Try plugging in x values that are very close to 7. Th range goes from negative infinity to some large positive number

[@albertobaiz2455]

Hi kris thanks again for this great video it help a lot, i will give [ln (22026.46580)] stars , health and prosperity be with always