sketch the following funciton and state the domain and range. y= 1/2 Sqr root ( 2x+4 ) -3 Please explain the domain and range with a little...

The domain of a function represents the input values.
 Here the domain stands for the x-values. Since the square root of a negative does not
exist in the real number system, 2x+4 must be greater than or equal to 0. So the domain
is found by solving the inequality:

class="AM">`2x+4>=0`

class="AM">`2x>=-4`

class="AM">`x>=-2`

The allowable
x-values must be greater than or equal to -2.

The range
represents the output of the function.  Here the range stands for the y-values. Since
x=-2 is the smallest value of x, the smallest value for y is found
by:

y=1/2 sqrt (2(-2)+4) -
3

y=1/2 sqrt (0) -
3

y=-3

The range of the
function is  class="AM">`y>=-3`

Here is a graph
that shows the graph exists for x's greater than or equal to -2 and y's greater than or
equal to -3.

src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-5,5,-5,5,1,1,1,1,1,300,200,func,.5 sqrt
(2x+4)-3,null,0,0,,,black,1,none"/>