Question

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

Answer 1

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`