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The domain of the function q(x) = x^4 - 4x^2 + 4 is [0,infinity). What is the range?

 May 28, 2021
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At  x  = 0,  y =  4

 

We  can find the first (and only) positive root  as

 

(x^2  - 2)^2   =  0

 

x^2  - 2   =  0

 

x^2   =  2          take  the positve root  

 

x  =   sqrt (2)

 

This root is of  a  multiplicity of  2   which  means  that  the  graph  touches  the  x  axis  at x = sqrt 2  but   does not pass through the   x axis.....and  the  graph to  the right of this  point is ever-increasing

 

So  the  range  =   the  domain  =  [0, inf )

 

See the  graph  here  :  https://www.desmos.com/calculator/6ary7m5ryp  

 

cool cool cool

 May 28, 2021
edited by CPhill  May 28, 2021

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