Finding the Height Function for y=\frac{-1}{X^2} + 4

In summary, y=\frac{1}{X^2}-1 has a function that has a max height of 3, y=\frac{-1}{X^2}+4 does not have a function that has a max height, but has a volume of 1.
  • #1
bayan
203
0
Hi guys.

I was doing a SAC and there were two questions

one was [tex]y=\frac {1}{X^2}-1[/tex] and the other was [tex]y=\frac {-1}{X^2}+4[/tex]

I got the hight function to be [tex]h=e^\frac{V}{\pi}-1[/tex] where V is the volume and max hight is 3 for the first function [tex]y=\frac {1}{X^2}-1[/tex]

Can someone help me to find the hight function of the other function please.


The Volume of both graphs are same.


Thanx in advance.
 
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  • #2
is this the hight function of second function? [tex]h=e^\frac{-V}{\pi}-4[/tex]
 
  • #3
would you mind defining a 'hight' function. I can find no references for it (other than misspelling it as height when it is defined for abelian groups according to planet math)
 
  • #4
bayan said:
Hi guys.

I was doing a SAC and there were two questions

one was [tex]y=\frac {1}{X^2}-1[/tex] and the other was [tex]y=\frac {-1}{X^2}+4[/tex]

[tex]y= \frac{1}{X^2}-1[/tex] is not a question- it is a function or equation. What was the question??

I got the hight function to be [tex]h=e^\frac{V}{\pi}-1[/tex] where V is the volume and max hight is 3 for the first function [tex]y=\frac {1}{X^2}-1[/tex]

Can someone help me to find the hight function of the other function please.


The Volume of both graphs are same.


Thanx in advance.

I didn't know a graph had a volume! I assume "hight" was a misprint for "height" but I'm still not sure what you mean by the "height" of a function.
 
Last edited by a moderator:
  • #5
HallsofIvy said:
[tex]y= \frac{1}{X^2-2}-1[/tex] is not a question- it is a function or equation. What was the question??



I didn't know a graph had a volume! I assume "hight" was a misprint for "height" but I'm still not sure what you mean by the "height" of a function.
Sorry about my BAD english but all I intended to say is how can I find the rate of change of height with respect to change in volume from the second equation.


Hope that makes it abit more clear.
 

1. What is the height function for y=\frac{-1}{X^2} + 4?

The height function for y=\frac{-1}{X^2} + 4 is a mathematical representation of the height or y-value of a point on the graph at a given x-value. It is calculated by taking the negative reciprocal of the square of the x-value and adding 4.

2. How do you find the height function for y=\frac{-1}{X^2} + 4?

To find the height function for y=\frac{-1}{X^2} + 4, you need to manipulate the given equation to isolate the y variable. This can be done by subtracting 4 from both sides and then taking the reciprocal of both sides. The resulting equation will be y=\frac{-1}{X^2}, which is the height function.

3. What is the domain of the height function for y=\frac{-1}{X^2} + 4?

The domain of the height function for y=\frac{-1}{X^2} + 4 is all real numbers except for 0. This is because the denominator cannot be equal to 0, as it would result in an undefined value.

4. How do you graph the height function for y=\frac{-1}{X^2} + 4?

To graph the height function for y=\frac{-1}{X^2} + 4, you can plot points by choosing different x-values and calculating the corresponding y-values using the height function equation. Another option is to create a table of values and plot the points on a graph. You can also use a graphing calculator to create a visual representation of the function.

5. What is the significance of the height function for y=\frac{-1}{X^2} + 4?

The height function for y=\frac{-1}{X^2} + 4 is significant because it allows us to calculate the y-values for any given x-value on the graph. It also helps us understand the behavior of the graph, such as the asymptotes and the maximum or minimum points. Additionally, it can be used to solve real-world problems and make predictions based on the height function's behavior.

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