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Find the range of the function
\(p(x) = \frac{x^2 + x + 1}{x^2 + 1}. \)

 Jun 24, 2019
 #1
avatar+106533 
+3

x^2 + x + 1

________

x^2  + 1

 

We would need Calculus  to determine this mathematically......a graph might work better 

 

Look here  :  https://www.desmos.com/calculator/ndujaokd6r

 

The max value for y  occurs at   (1, 1.5)

And the minimum value for y occurs at  (-1, 0.5)

And all y values between these are defined

 

So.....the range is   [ 0.5, 1.5 ]

 

 

cool cool cool

 Jun 24, 2019
edited by CPhill  Jun 24, 2019
 #2
avatar+91 
+1

Thanks :)

Pushy  Jun 25, 2019

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