Hopefully by "domain" you mean the intervals that we've been finding by taking the derivative of an equation and setting it equal to zero, solving for x to get x-values, and setting up intervals from there..because that is what I'm getting out of this. Well...now that I think about it, yes, that must be what that means haha. Domain does involve x-values, whereas range involves y-values. **Let's say for example you were given the equation f(x)=4x^2+24x+9 and the directions told you to find the DOMAIN. Welllllll, thinking back to good ole advanced math, you should remember that the domain for ALL POLYNOMIALS is: (-infinity,infinity) so, that would be your domain. *Also, if you were asked for the range, that would be (-infinity,infinity) also, because that is the rule for polynomials. *Next, let's say you're given the equation (9x+7)/(6x+3)...which is indeed a fraction. Again, thinking back to advanced math, different rules apply for finding the domain for fractions. The rules say you must take the bottom of the fraction, set it equal to zero and solve for x (for the first step). -once you solve for x for the equation 6x+3 you should get -1/2 -next, you set up intervals with the x-value you found. So you should have: (-infinity,-1/2) u (-1/2,infinity) and that's all you do!
**Now to know if a function is increasing or decreasing, that gives you a hint that you're going to have to use the First Derivative Test most likely..which says you take the derivative of the equation, set it equal to zero, solve for x, set up intervals, and plug values in between the intervals(plugging into the derivative) to find out if the number is negative or positive (negative=decreasing; positive=increasing) **Sooo, using another equation: (4x^2)/(3x+1)let's find where it's increasing or decreasing. *First, let's take the derivative of it...for the first step you should get this: (3x+1)(8x)-[(4x^2)(3)]/(3x+1)^2 Simplifying that you should end up with: (12x^2+8x)/(3x+1)^2 *Now, since it's a fraction, you only take the numerator and set it equal to zero and solve for x. *So you have 12x^2+8x=0 4x(3x+2)=0 factor out a 4x 4x=0 3x+2=0 x=0,-2/3 *So now that you have your x-values, you set up your intervals starting with negative infinity and the smallest value out of the two, which would be -2/3 *So for your intervals you should have: (-infinity,-2/3)u(-2/3,0)u(0,infinity) *Now you plug in values for each interval(into the derivatve 12x^2+8x/(3x+1)^2 *So for the first interval you can plug in -1...and you would end up with a positive number. So that means the function is increasing on (-infinity,-2/3) *Now for the 2nd interval you can plug in -1/2...and you would get a negative number. So that means that the function is decreasing on (-2/3,0) *And for the last interval you can plug in 1...and you should get a positive number again. And that means that the function is increasing on (0,infinity) also
The domain of a graph is all possible x’s or critical numbers. We’ve used this many times, even if we didn’t realize it, as intervals. When we set up intervals for a function, that is also its graph’s domain. For example:
Find the domain of… 1) y = x (-infinity, infinity)
2) y = square root of x (0, infinity) *because you can’t have a negative inside of a square root (you’ll get i)
3) y = 1/x (-infinity, 0) u (0, infinity) **because you can’t have a 0 on the bottom of a fraction (you’ll get undefined)
For more complex equations, to find the domain, take the derivative, set it equal to 0, and solve for x. The x-values you get are your critical numbers that you use to set up your intervals. (This is part of the First Derivative Test.)
To figure out if a function is increasing or decreasing, simply plug in any value between the two end points of your interval into the derivative of your function and solve. (This is also part of the First Derivative Test.) If you get a positive number, it is increasing. If you get a negative number, it is decreasing. ***When a function is increasing, then decreasing, it is a max. ****When a function is decreasing, then increasing, it is a min.
Example: 4) f(x) = x^2 f’(x) = 2x 2x = 0 x = 0 (-infinity, 0) u (0, infinity) f(-1) = 2(-1) = -2 f(1) = 2(1) = 2 This graph is decreasing at (-infinity, 0) and increasing at (0, infinity).
finding the domain of a graph can be remembered as finding all "x" values for which the graph is valid or exists. For majority of graphs the domain is negative infinity to positive infinity.
Example #1 any line like,
y = 8x + 9
can take any possible x value, positive or negative. The domain is then all x numbers, or you can say the domain is negative infinity to positive infinity.
example #2:
y = sqrt(x)
you can not take all numbers, because the square root of a negative number is undefined (or not real). Therefore, the domain of this function is x >=0, or you can say that the domain is 0 to infinity.
example #3:
y = 1/x
this equation is existing at all numbers EXCEPT 0. So then the domain is all numbers except 0, or you could say it's negative infinity to 0 and 0 to infinity.
How do you know if a functions is increasing or decreasing? When asked to find out whether a function is increasing or decreasing you must follow the steps to finding a reletive max or min or use the steps of the first derivative test because the steps for each of these are the same and they each allow you to find the intervals to which the functions is increasing or decreasing
The steps to solving whether the function is increasing or decreasing are: Take derivative and set equal to zero Solve for x Set up intervals (-infinity, pt)U(pt, infinity) Plug in value on the interval into the derivative ((if you get a positive number the function is increasing, If you get a negative number the function is decreasing)) (( A max is increasing then decreasing, A min is decreasing then increasing))
Example: Find the open intervals on which f(x)= x^3-3/2x^2 is increasing or decreasing Take derivative and set equal to zero 3x^2-3x=0 Solve for x 3x(x-1)=0 X=0,1 Set up intervals (-infinity, pt)U(pt, infinity) (negative infinity,0)U(0,1)U(1,infinity) Plug in value on the interval into the derivative F’(-1)= 3(-1)^2-3(-1)=6 Positive therefore increasing F’(1/2)= 3(1/2)^2-3(1/2)= -3/4 Negative therefore decreasing F’(2)= 3(2)^2-3(2)= 6 Positive therefore increasing Therefore increasing: (negative infinity, 0) U (1, infinity) Decreasing: (0,1)
How can you find the domain of a graph? To find the domain without a graph given, you must solve for where a function can’t exist. So, if for instance you have a function where you have x^3 over x^2+8x-20, you analyze the denominator for where it will equal zero. Where you have a points in your denominator that equal zero, you have points on your graph that can't exist.
In the example, factoring the denominator gives you (x+10)(x-2), solve for 0, so you get -10 and +2. Now plug the numbers -9 and +1 into the that same equation, if you get any number for an answer that isn't zero, you have proven that the numbers in between -10 and +2 do exist.
Build your domain:
You know it can exist from (- infinity, -10)(-10, 2) and (2, infinity). **A function CAN'T exist by placing in () versus [], where [] means that the values would be included, and existing.
To find the domain with a given graph: Often times, if you are given a graph you just look at the line, see where it begins, see where it ends, look for any points where the line has an asymptote (point where it cannot exist). If I were to graph the above example from the interval [-13, 13] you would be able to tell me the function existed at [-13, -10)(-10, 2)(2, 13] just by noticing that the line doesn't exist at the points where x= -10 and +2.
How do you know if a functions is increasing or decreasing? You can tell if a function is increasing or decreasing by graphing it and then looking at the graph. You can also tell by looking at the max’s or min’s, which can be found by first derivative test. A graph is increasing when the slope is positive, and decreasing when the slope is negative. That is, when the curve is like / it's increasing, and when it's like \ it's decreasing.
How can you find the domain of a graph? The domain of a graph is all possible x’s or critical numbers. We’ve used this before as intervals. When we set up intervals for a function, that is also its graph’s domain.
How do you know if a functions is increasing or decreasing? You can tell if a function is increasing or decreasing by graphing it and then looking at the graph. You can also tell by looking at the maxs or mins, which can be found by first derivative test. A graph is increasing when the slope is positive, and decreasing when the slope is negative.
How can you find the domain of a graph? The domain of a graph is all possible x’s or critical numbers. You set the numbers on a interval and then thats your domain. It would be set up as (- infinity, #) u (#, infinity).
How do you know if it is increasing or decreasing? You plug in the numbers that are more and less than the critical numbers then if it is positive then it is increasing and if it is negative then it is decreasing. You could also look at the graph and whatever it says is the answer basically.
domain??? look at the graph and see where it stops and ends, I guess
if it's increasing or decreasing depends on whether the number plugged into an interval after you find the derivative and the intervals in certain cases
I really don't know how to give examples of them tbh.....
How to find the domain of a graph. The domain of a graph is the critical numbers. You would have to take the derivative of the equation of the function then, use the same steps you would use to find the critical numbers.
How to find if its increasing or decreasing. You would use the first derivative test. First you would have to find the critical numbers of the function. You would use the normal steps neccessary. Then you would set up your intervals. You would take a number from each interval and plug that number in for your variable in the derivative of the equation of the function. If you get an even answer then at that interval the graph is increasing. If you get a negative number then at that interval the grpah is decreasing. If you get zero then the test fails.
Hopefully by "domain" you mean the intervals that we've been finding by taking the derivative of an equation and setting it equal to zero, solving for x to get x-values, and setting up intervals from there..because that is what I'm getting out of this. Well...now that I think about it, yes, that must be what that means haha. Domain does involve x-values, whereas range involves y-values.
ReplyDelete**Let's say for example you were given the equation f(x)=4x^2+24x+9 and the directions told you to find the DOMAIN. Welllllll, thinking back to good ole advanced math, you should remember that the domain for ALL POLYNOMIALS is:
(-infinity,infinity) so, that would be your domain. *Also, if you were asked for the range, that would be (-infinity,infinity) also, because that is the rule for polynomials.
*Next, let's say you're given the equation (9x+7)/(6x+3)...which is indeed a fraction. Again, thinking back to advanced math, different rules apply for finding the domain for fractions. The rules say you must take the bottom of the fraction, set it equal to zero and solve for x (for the first step).
-once you solve for x for the equation 6x+3 you should get -1/2
-next, you set up intervals with the x-value you found. So you should have:
(-infinity,-1/2) u (-1/2,infinity) and that's all you do!
**Now to know if a function is increasing or decreasing, that gives you a hint that you're going to have to use the First Derivative Test most likely..which says you take the derivative of the equation, set it equal to zero, solve for x, set up intervals, and plug values in between the intervals(plugging into the derivative) to find out if the number is negative or positive (negative=decreasing; positive=increasing)
**Sooo, using another equation:
(4x^2)/(3x+1)let's find where it's increasing or decreasing.
*First, let's take the derivative of it...for the first step you should get this:
(3x+1)(8x)-[(4x^2)(3)]/(3x+1)^2
Simplifying that you should end up with:
(12x^2+8x)/(3x+1)^2
*Now, since it's a fraction, you only take the numerator and set it equal to zero and solve for x.
*So you have 12x^2+8x=0
4x(3x+2)=0 factor out a 4x
4x=0 3x+2=0
x=0,-2/3
*So now that you have your x-values, you set up your intervals starting with negative infinity and the smallest value out of the two, which would be -2/3
*So for your intervals you should have:
(-infinity,-2/3)u(-2/3,0)u(0,infinity)
*Now you plug in values for each interval(into the derivatve 12x^2+8x/(3x+1)^2
*So for the first interval you can plug in -1...and you would end up with a positive number. So that means the function is increasing on (-infinity,-2/3)
*Now for the 2nd interval you can plug in -1/2...and you would get a negative number. So that means that the function is decreasing on (-2/3,0)
*And for the last interval you can plug in 1...and you should get a positive number again. And that means that the function is increasing on (0,infinity) also
This comment has been removed by the author.
ReplyDeleteThe domain of a graph is all possible x’s or critical numbers. We’ve used this many times, even if we didn’t realize it, as intervals. When we set up intervals for a function, that is also its graph’s domain. For example:
ReplyDeleteFind the domain of…
1) y = x
(-infinity, infinity)
2) y = square root of x
(0, infinity)
*because you can’t have a negative inside of a square root (you’ll get i)
3) y = 1/x
(-infinity, 0) u (0, infinity)
**because you can’t have a 0 on the bottom of a fraction (you’ll get undefined)
For more complex equations, to find the domain, take the derivative, set it equal to 0, and solve for x. The x-values you get are your critical numbers that you use to set up your intervals. (This is part of the First Derivative Test.)
To figure out if a function is increasing or decreasing, simply plug in any value between the two end points of your interval into the derivative of your function and solve. (This is also part of the First Derivative Test.) If you get a positive number, it is increasing. If you get a negative number, it is decreasing.
***When a function is increasing, then decreasing, it is a max.
****When a function is decreasing, then increasing, it is a min.
Example:
4) f(x) = x^2
f’(x) = 2x
2x = 0
x = 0
(-infinity, 0) u (0, infinity)
f(-1) = 2(-1) = -2
f(1) = 2(1) = 2
This graph is decreasing at (-infinity, 0) and increasing at (0, infinity).
How can you find the domain of a graph?
ReplyDeletefinding the domain of a graph can be remembered as finding all "x" values for which the graph is valid or exists. For majority of graphs the domain is negative infinity to positive infinity.
Example #1
any line
like,
y = 8x + 9
can take any possible x value, positive or negative. The domain is then all x numbers, or you can say the domain is negative infinity to positive infinity.
example #2:
y = sqrt(x)
you can not take all numbers, because the square root of a negative number is undefined (or not real). Therefore, the domain of this function is x >=0, or you can say that the domain is 0 to infinity.
example #3:
y = 1/x
this equation is existing at all numbers EXCEPT 0. So then the domain is all numbers except 0, or you could say it's negative infinity to 0 and 0 to infinity.
http://www.youtube.com/watch?v=I0f9O7Y2xI4
http://www.ehow.com/video_4756698_define-domain-graph.html
How do you know if a functions is increasing or decreasing?
When asked to find out whether a function is increasing or decreasing you must follow the steps to finding a reletive max or min
or use the steps of the first derivative test
because the steps for each of these are the same and they each allow you to find the intervals to which the functions is increasing or decreasing
The steps to solving whether the function is increasing or decreasing are:
Take derivative and set equal to zero
Solve for x
Set up intervals (-infinity, pt)U(pt, infinity)
Plug in value on the interval into the derivative ((if you get a positive number the function is increasing, If you get a negative number the function is decreasing)) (( A max is increasing then decreasing, A min is decreasing then increasing))
Example:
Find the open intervals on which f(x)= x^3-3/2x^2 is increasing or decreasing
Take derivative and set equal to zero
3x^2-3x=0
Solve for x
3x(x-1)=0
X=0,1
Set up intervals (-infinity, pt)U(pt, infinity)
(negative infinity,0)U(0,1)U(1,infinity)
Plug in value on the interval into the derivative
F’(-1)= 3(-1)^2-3(-1)=6
Positive therefore increasing
F’(1/2)= 3(1/2)^2-3(1/2)= -3/4
Negative therefore decreasing
F’(2)= 3(2)^2-3(2)= 6
Positive therefore increasing
Therefore increasing: (negative infinity, 0) U (1, infinity)
Decreasing: (0,1)
How can you find the domain of a graph?
ReplyDeleteTo find the domain without a graph given, you must solve for where a function can’t exist. So, if for instance you have a function where you have x^3 over x^2+8x-20, you analyze the denominator for where it will equal zero. Where you have a points in your denominator that equal zero, you have points on your graph that can't exist.
In the example, factoring the denominator gives you (x+10)(x-2), solve for 0, so you get -10 and +2. Now plug the numbers -9 and +1 into the that same equation, if you get any number for an answer that isn't zero, you have proven that the numbers in between -10 and +2 do exist.
Build your domain:
You know it can exist from (- infinity, -10)(-10, 2) and (2, infinity). **A function CAN'T exist by placing in () versus [], where [] means that the values would be included, and existing.
To find the domain with a given graph:
Often times, if you are given a graph you just look at the line, see where it begins, see where it ends, look for any points where the line has an asymptote (point where it cannot exist). If I were to graph the above example from the interval [-13, 13] you would be able to tell me the function existed at [-13, -10)(-10, 2)(2, 13] just by noticing that the line doesn't exist at the points where x= -10 and +2.
http://answers.yahoo.com/question/index?qid=20081208081025AAHFvaZ
How do you know if a functions is increasing or decreasing?
You can tell if a function is increasing or decreasing by graphing it and then looking at the graph. You can also tell by looking at the max’s or min’s, which can be found by first derivative test. A graph is increasing when the slope is positive, and decreasing when the slope is negative. That is, when the curve is like / it's increasing, and when it's like \ it's decreasing.
This comment has been removed by the author.
ReplyDeleteHow can you find the domain of a graph?
ReplyDeleteThe domain of a graph is all possible x’s or critical numbers. We’ve used this before as intervals. When we set up intervals for a function, that is also its graph’s domain.
How do you know if a functions is increasing or decreasing?
You can tell if a function is increasing or decreasing by graphing it and then looking at the graph. You can also tell by looking at the maxs or mins, which can be found by first derivative test. A graph is increasing when the slope is positive, and decreasing when the slope is negative.
How can you find the domain of a graph?
ReplyDeleteThe domain of a graph is all possible x’s or critical numbers. You set the numbers on a interval and then thats your domain. It would be set up as (- infinity, #) u (#, infinity).
How do you know if it is increasing or decreasing?
You plug in the numbers that are more and less than the critical numbers then if it is positive then it is increasing and if it is negative then it is decreasing. You could also look at the graph and whatever it says is the answer basically.
domain???
ReplyDeletelook at the graph and see where it stops and ends, I guess
if it's increasing or decreasing depends on whether the number plugged into an interval after you find the derivative and the intervals in certain cases
I really don't know how to give examples of them tbh.....
How to find the domain of a graph. The domain of a graph is the critical numbers. You would have to take the derivative of the equation of the function then, use the same steps you would use to find the critical numbers.
ReplyDeleteHow to find if its increasing or decreasing. You would use the first derivative test. First you would have to find the critical numbers of the function. You would use the normal steps neccessary. Then you would set up your intervals. You would take a number from each interval and plug that number in for your variable in the derivative of the equation of the function. If you get an even answer then at that interval the graph is increasing. If you get a negative number then at that interval the grpah is decreasing. If you get zero then the test fails.