Expert: Paul Klarreich - 9/18/2007

Question
How do I graph the domain; f(x)=square root of 4x+4

Answer
Questioner:   walter
Category:  Advanced Math
Private:  No
 
Subject:  algebra
Question:  How do I graph the domain; f(x)=square root of 4x+4
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Hi, Walter,

First step:  Figure out what the domain IS.  For a function like this, you want the set of all x where the function is defined and real (i.e. not imaginary).

f(x) = sqrt(4x+4)

If the 'radicand' (the expression under the radical symbol) is negative, you will get an imaginary number -- a no-no.  So you require:

4x + 4 >= 0  [Mathematicians read '>=0' as 'is nonnegative.']

x + 1 >= 0

    x >= - 1

Now the graph of  x >= -1 is a subset of the number line; it consists of all points to the right of and including  x = -1.  So you graph it:

=======================================================
WARNING: USE COURIER FONT TO VIEW THIS
===================================================


             *------------------------------->
----+----+----+----o----+----+----+----+----+----
  -3   -2   -1    0    1    2    3    4    5

(On paper, you make a solid circle above x = -1 to indicate that the point is included as part of the domain.)