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Find the range of the function.f(x) = x2 + 3

Find the range of the function.f(x) = x2 + 3-example-1
User Misticos
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We have the following function given:


y=x^2+3

The domain is all the possible values for x in the function and as we can see we don't have any restriction so then the domain would be all the reals.


D=R=(-\infty,\infty)

And for the range we need to take in count that we have a parabola open upward so then the minimum value would be the vertex given by:


V_x=-(b)/(2a),a=1,b=0,c=3
V_x=-(0)/(2\cdot1)=0

And the y minimum value would be:


V_y=(0)^2+3=3

Then the range would be given by:


\text{Range}=\left\lbrack 3,\infty\rbrack\right?=y\ge3

Final answer:


y\ge3

User Guadalupe
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