Board 8 > how do you find the range of a function with no calculator

(+) Yeah! (+)

so say the function is root(2-x)


the domain is [2,infinity)

the range is [0,infinity)

how do you find the range for this function, or for any function, with no calculator?

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KA POWIE

that is not the domain

but to figure it out - try plotting some points and finding a pattern, and points where it stops working

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I'm always serious. Otherwise, no one will take me seriously.

For a continuous function, you just plug in the bounds of the domain into the function and see what you get

domain: [2, inf)
root(2-2) = 0
therefore range: [0, inf)

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_foolmo_
[NO BARKLEY NO PEACE]

Inspection? For real numbers, square roots can only evaluate to non-negative numbers, so the range of the function only includes positive numbers. Just graph it by hand and see where it falls.

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No amount of planning will ever replace dumb luck.

foolm0ron posted...
For a continuous function, you just plug in the bounds of the domain into the function and see what you get

domain: [2, inf)
root(2-2) = 0
therefore range: [0, inf)

nah, a continuous function could be like y=x^2, where the bounds of the domain would give you an incomplete picture

(though of course, that approach does seem to work here

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I'm always serious. Otherwise, no one will take me seriously.

I literally just did this in my homework (but with clean roots)

Because the function creates a semicircle y^2+x^2=2 (work backwards to get this if you need to), you know that the domain is [-root 2, root 2] and because it's the positive half of the semicircle (positive y values), the range is [0, root 2].

i have a headache though so this explanation probably isn't going to help you at all except give you the answer

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~Acting on Impulse~
Black Turtle still didn't MAJORA'S MASK

Formally, for a continuous function or piece-wise continuous you can find the y-coordinates of its endpoints (or the limit it approaches at +/- infinity, and at any domain boundaries excluded from the domain itself), the y-coordinates of the endpoints of its pieces (e.g. the vertex of an absolute value function) and the y-coordinates of its critical points (by setting its derivative to zero), and fill in the range between any two points which are connected continuously.

Often, however, inspection or some knowledge of the underlying functions (e.g. root(x) has a range of [0, infinity)) and transformations (e.g. f(x)+3 will raise all points in the range by +3) will serve you well. Knowing the general behaviour of polynomials (especially linear functions and parabolas), roots, reciprocals, exponents, logs, trig functions, and absolute value functions is typically helpful, though which ones you will need to know will depend on the course/application.

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so there's no set way of finding the range (When i dont have a calculator)? I just have to have a good knowledge of my functions/graphs?

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KA POWIE

Shouldn't the domain be from negative infinity to 2?

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Sack Up Or Shut Up™

yeah, i think i messed that up..

is there a way to find range for a function without a calculator?

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KA POWIE

I'm not familiar with any systematic way, and if one exists, I imagine it'd be more difficult to understand than what you're doing.

Math isn't all just calculation and going through the same processes over and over again, though this is how it tends to be taught unfortunately. Sometimes you need to be able just to sit back and think something through and not go through a rote series of steps to solve a problem because it's exactly like the five versions of the problem you saw doing the homework assignment.

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No amount of planning will ever replace dumb luck.

You can find all local minima and maxima of a continuous function in its domain and any vertical asymptotes and examine the function around those.

The formal definition of the range is all values y in the co-domain for which f(x) = y for some x in the domain. If the function is discrete, you can evaluate them all, and if it's continuous, you just examine it like I described above.

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TheFlyingWolfen posted...
so there's no set way of finding the range (When i dont have a calculator)? I just have to have a good knowledge of my functions/graphs?

Finding the range is, in general, not a simple problem.

Let me ask you a question, though: how does a calculator even help you (unless it's like...a graphing calculator)? It strikes me that calculators don't actually deal with the hard part of the problem.

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Cats land on their feet. Toast lands peanut butter side down. A cat with toast strapped to its back will hover above the ground in a state of quantum indecision

by getting a job and buying a calculator

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