How to Find the Domain and Range of √(H^2 + 12756H)?

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Homework Help Overview

The discussion revolves around finding the domain and range of the function √(H^2 + 12756H) algebraically. Participants are exploring the conditions under which the expression inside the square root is non-negative, which is essential for determining the domain and range.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the conditions for the function to be defined, particularly focusing on when H^2 + 12756H is less than zero. There are inquiries about solving the equation H^2 + 12756H = 0 and whether it can be approached algebraically or requires graphical interpretation.

Discussion Status

There is an ongoing exploration of algebraic methods to determine the domain and range. Some participants suggest that the quadratic formula may be necessary, while others propose that understanding the sign of the product H(H + 12756) could lead to insights about the domain. Multiple interpretations of how to approach the problem are being discussed.

Contextual Notes

Participants are considering the implications of the quadratic nature of the function and the requirement for the expression under the square root to be non-negative. There is uncertainty about the algebraic methods available and the extent to which graphical analysis can aid in understanding the problem.

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Homework Statement



I have the function H^2 + 12756H and I want to find the domain and range of it's square root algebraically.

Homework Equations

The Attempt at a Solution



I understand y= √(H^2 + 12756H) is undefined if H^2 + 12756H < 0, however I don't get how to find its domain and range using algebra. Maybe someone can help me.
 
Last edited:
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zaddyzad said:

Homework Statement



I have the function H^2 + 12756H and I want to find the domain and range of it's square root algebraically.

Homework Equations



The Attempt at a Solution



I understand y= √(H^2 + 12756H) is undefined if H^2 + 12756H < 0, however I don't get how to find its domain and range using algebra. Maybe someone can help me.
Can you solve for H2 + 12756H = 0 ?

If you graph y = H2 + 12756H you get a continuous graph. H2 + 12756H cannot change sign without going through zero.

All of that should help you.
 
I understand how to find the domain and range of the root function by looking at the original graph, however my question is can it be done algebraically, if so how?

And no I don't believe you can solve for H with 0 = h^2 + 12756h algebraically only with quadratic formula. The point of this post is to find out the easiest way to solve this sort of thing for domain, and would it be finding x-intercepts and deriving your domain of the root from that ?
 
Last edited:
zaddyzad said:
I understand how to find the domain and range of the root function by looking at the original graph, however my question is can it be done algebraically, if so how?

And no I don't believe you can solve for H with 0 = h^2 + 12756h algebraically only with quadratic formula. The point of this post is to find out the easiest way to solve this sort of thing for domain, and would it be finding x-intercepts and deriving your domain of the root from that ?
How purely algebraic do you want the solution to be?

Yes, it can be done!
 
zaddyzad said:

Homework Statement



I have the function H^2 + 12756H and I want to find the domain and range of it's square root algebraically.


Homework Equations




The Attempt at a Solution



I understand y= √(H^2 + 12756H) is undefined if H^2 + 12756H < 0, however I don't get how to find its domain and range using algebra. Maybe someone can help me.
H^2+ 12756H= H(H+ 12756)< 0 and the product of two numbers is negative if and only if the numbers are of opposite sign.
So either H< 0 and H+ 12756> or H> 0 and H+ 12756< 0.
(Only one of those is actually possible.)
 

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