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i dont understand how to do these.
are there important key rules i need to keep in mind?!
help me out here?
what should i look for?

ex: f(x)= squareroot x^2 +4

ex2: f(x)= x/x^2-5x

2006-08-10 12:14:34 · 4 answers · asked by AT 2 in Science & Mathematics Mathematics

4 answers

In a function such as f(x), the domain of the function consists of the set of all values of x (the independent variable) for which the function exists.

The range of a function is the set of all values that the function can assume as x assumes all values in its domain.

In your examples:

f(x) = sqrt(x²+4) you need to remember that whatever you're taking the square root of needs to be ≥ 0 because you haven't as yet learned to deal with square roots of negative values.

This function has, for its domain, all values of x positive or negative. Since squaring a negative produces a positive, the value (x²+4) will always be ≥ 4 and there will be no problems.

How about the range of f(x)? since the smallest value for the function is obtained when x = 0 (that is f(0) = 2) it is pretty clear that f(x) ≥ 2 for all x.

If you teacher only wants the principle value of the range, then you're finished. But it pays to remember that sqrt(x) always has two values, positive and negative (since the product of two negative numbers is positive) so the total range of the cunction is

f(x) ≤ -2 and fx) ≥ 2

In the 2'nd example, you need to worry about values for which the denominator of the fraction (x²-5x) can be 0.

A quick examination reveals that, at x = 0 and x = 5 the denominator goes to zero.

In the first case (at x = 0) the denominator also goes to 0 and so the function becomes 0/0 which is undefined. There is literally a 'hole' in the graph at x = 0.

In the 2'nd case (at x = 5) the fraction goes to 5/0 (which is also undefined) but it does so in a completely different way.

In the 1'sr case, the value of the function gets closer and closer to -1/5 as x gets closer and closer to zero. And it makes no difference if we approach 0 from the negative side (written lim(f(0-))) or from the positive side (written lim(f(0+))). The function gets closer and closer to -1/5 either way. This is called a 'simple' or 'removeable' singularity.

In the 2'nd case, lim(F(5-)) becomes unboundedly large in the negative direction while lim(f(5+)) becomes unboundedly large in the positive direction. Again, the function fails to exist at x = 5 but, since lim(f(5-)) is not equal to lim(f(5+)) it is called an 'essential' singularity.

Hope all of that helps.


Doug

2006-08-10 14:48:38 · answer #1 · answered by doug_donaghue 7 · 0 0

DOMAIN IS ALL THE Y VALUE IN THE PROBEM> AND RANGE IS ALL THE X. so want # can u put for x in the problem. And Y is all the answer it can be. FOR EX 1 x could be all number except negative because if you plug negative in -x^2 + 4 = indufined or no soultion u can't slove it. The domain is all postive # becuase that will make the statement ture. The range will all# >than or eual to 5 bececause the lowest postive number you can put is 1 (0 made it undifind because 0 * 0 ===0 its not true.).THat how i think of it. MAKE SURE TO GIVE ME 10 POINTS FOR THE HELP I WANT TO GET TO LEVEL 2.

2006-08-10 13:35:38 · answer #2 · answered by Best Helper 4 · 0 0

I am assuming that you are using only real numbers.

The rules that you need to remember:
1) No negative numbers under an even index radical ( square root, 4th-root, ... )
2) No zero denominator.
3) No nonpositive numbers in a logarithm.

For your two examples, this would mean something like:

f(x) = sqrt( x^2 + 4 )
the stuff under the square root is the whole "x^2 + 4"
Thus you need to look at the inequality
x^2 + 4 >= 0
The solutions are the values in the domain.


f(x) = x/(x^2 - 5x)
The stuff in the denominator is "x^2-5x". Thus we must see when this is zero:

x^2-5x = 0
The solutions are the numbers that are NOT in the domain.

2006-08-10 13:01:29 · answer #3 · answered by AnyMouse 3 · 0 0

area is how far the equation can stretch around the x-axis selection is how far the equation can stretch around the y-axis A function is an equation that has all genuine solutions. subsequently sure, it extremely is a function. The area and selection are all genuine numbers.

2016-11-04 07:51:42 · answer #4 · answered by ? 4 · 0 0

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