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=-\frac{b}{2a},a=1,b=0,c=3$$V_x=-\frac{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:

$y\ge3$