testing header
Math Goodies is a free math help portal for students, teachers, and parents.
Free Math
Newsletter
 
 
Interactive Math Goodies Software

Buy Math Goodies Software
testing left nav
Math Forums @ Math Goodies
Math Forums @ Math Goodies
Home | Profile | Register | Active Topics | Members | Search | FAQ
Username:
Password:
Save Password
Forgot your Password?

 All Forums
 Homework Help Forums
 Algebra
 Finding the range
 New Topic  Reply to Topic
 Printer Friendly
Author Previous Topic Topic Next Topic  

moon1130
Senior Member

USA
24 Posts

Posted - 03/26/2013 :  23:39:35  Show Profile  Reply with Quote
I am asked to find the range of the function h(t)=(9-t). I solved the problem by first finding the domain of h, which is -3t3, and then calculating the range from this via a table. I am sure that there is another way to solve this problem algebraically by dealing directly with the range concept (and bypassing the domain), but I have not been able to find it. Can someone help me?

Thank you.
Go to Top of Page

royhaas
Moderator

USA
3059 Posts

Posted - 03/27/2013 :  08:22:11  Show Profile  Reply with Quote
By definition, the range is the set of values corresponding to the domain. In this case, it's [0,3].
Go to Top of Page

the_hill1962
Advanced Member

USA
1468 Posts

Posted - 03/27/2013 :  10:39:06  Show Profile  Reply with Quote
The way that you stated is really is a good way to solve it. There is no "algebraic" method. (9-t) does not simplify anyway.
For these type of problems, looking for discontinuities (holes or asymptotes, etc) is the way answer it.
Sometimes a table might not show the discontinuities.
Please let us know what you list for the answer to this problem so we can check to make sure you did it correctly.
Go to Top of Page

Ultraglide
Advanced Member

Canada
299 Posts

Posted - 03/27/2013 :  11:02:59  Show Profile  Reply with Quote
An alternate way of looking at this problem is by graphing the function.
First note that y=9-t is a parabola opening downward with t-intercepts of 3 and an h-intercept of 9.
This function, though, is a square root function, so you are restricted to positive values, hence any part of the function below the t-axis is eliminated.
So now you only have h-values between 0 and 9 so if you take the root, you get values between 0 and 3.
Go to Top of Page

moon1130
Senior Member

USA
24 Posts

Posted - 03/30/2013 :  23:47:10  Show Profile  Reply with Quote
I thank each of you for your responses and help. I now understand the process. I cannot put my finger on what exactly confused me earlier, but it is all clear in my mind now.

My answer to this question is [0,3] also. I determined the range by first finding the domain and them calculating the h(t) values for the minimum and maximum range values, respectively.

I was looking for an algebraic method akin to finding the inverse of a one-to-one function.

All of you have a very Good one...

moon1130
Go to Top of Page

Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 03/31/2013 :  12:28:29  Show Profile  Reply with Quote
quote:
Originally posted by Ultraglide

An alternate way of looking at this problem is by graphing the function.
First note that y=9-t is a parabola opening downward with t-intercepts of 3 and an h-intercept of 9.
This function, though, is a square root function, so you are restricted to positive values, hence any part of the function below the t-axis is eliminated.
So now you only have h-values between 0 and 9 so if you take the root, you get values between 0 and 3.



The function is h(t) = (9 -t)

Thus it is the upper half of a circle

h = 9 - t → h + t = 3

Edited by - Subhotosh Khan on 03/31/2013 12:30:12
Go to Top of Page

Ultraglide
Advanced Member

Canada
299 Posts

Posted - 04/02/2013 :  18:02:40  Show Profile  Reply with Quote
Oops, you're right it is a semi-circle but everything else is the same.
Go to Top of Page
  Previous Topic Topic Next Topic  
 New Topic  Reply to Topic
 Printer Friendly
Jump To:
Math Forums @ Math Goodies © 2000-2004 Snitz Communications Go To Top Of Page
This page was generated in 0.06 seconds. Snitz Forums 2000
testing footer
About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page




Copyright © 1998-2014 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 21 Oct 2014