1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Range of a Function

  1. Mar 18, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the range of h

    2. Relevant equations

    h(x) = sqrt(25 + (x - 3)2)

    3. The attempt at a solution

    I factored out the (x-3)2 and simplified to get

    sqrt(x2 - 6x + 34)

    I was trying to figure out the domain first, knowing that x2 - 6x >= -34 in order for the number inside the sqrt to be non-negative.. I don't know, maybe I'm missing something really basic here. Help? :)
  2. jcsd
  3. Mar 18, 2010 #2


    Staff: Mentor

    Let's get the terminology straight. You expanded (x-3)2 ; it was already factored.
    The best thing, IMO, was to leave the radicand in its given form, 25 + (x-3)2. Looking at that as its own function, what is the range of this function? That will tell you a lot about the range of h(x).
  4. Mar 18, 2010 #3
    Well the range of 25 + (x - 3)2 is y >= 25, right? So, the range of sqrt(25 + (x - 3)2 is y >= 5?

    Yea, I think expanding the (x - 3)2 term messed me up. I was thinking that i was possible for the radicand to be a negative number.. ugh. Stupid mistake.

    Thanks a lot for the help.
  5. Mar 18, 2010 #4

    Char. Limit

    User Avatar
    Gold Member

    Also, just to let you know...

    x^2-6x has a minimum of -9. It will never be less than -34.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Range Function Date
Domain and Range of a Function and Its Inverse- Polynomials Feb 5, 2018
Range of a weird function Jan 28, 2017
Range of composite function Nov 21, 2016
Domain and range help Aug 2, 2016
Function range Apr 25, 2016