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 Feb 9, 2018
 #1
avatar+102422 
+1

1.  f(x)  =   3√x   +  2

 

We can put in any real number for x.....so the domain  is just  (-inf, inf)

 

And any real  number can be generated from the function

 

So.....the range is also   (-inf, inf)

 

Here's the graph  :  https://www.desmos.com/calculator/sd0menwuyg

 

 

cool cool cool

 Feb 9, 2018
 #2
avatar+102422 
+1

2.  f(x)  =  2 √x

 

Note that we cannot put any negative values in the square root  [ this generates a non-real number ]

 

So  the domain is   [ 0, inf )

 

And  out of a positive square root, we can never get any  negative values

 

So.....the range is the same   [0, inf )

 

Here's a graph : https://www.desmos.com/calculator/hndidezpmc

 

 

cool cool cool

 Feb 9, 2018
 #3
avatar+102422 
+1

3.   f(x)  =  3√x      ⇒   f(x)  =  -23√x  -  1

 

The  "-"  out front reflects the  graph across the x axis

 

The "2"  "vertically stretches " the graph away from the x axis

 

The  "-1"  at the end shifts the graph down 1 unit

 

 

cool cool cool

 Feb 9, 2018

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