Question

Find the range of f(x)=3x^2+3

Answer 1

`[3,\infty)`

Explanation:

`f(x)=3x^2+3\\\\f(x)=3(x-0)^2+3`

`\y\:\text{or} [3,\infty)`

Answer 2

`\mathrm{Range\:of\:}3x^2+3:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:3\:\\ \:\mathrm{Interval\:Notation:}&\:[3,\:\infty \:)\end{bmatrix}`

Function range definition:

• The set of values of the dependent variable for which a function is defined.

Vertex of
`3x^(2) +3`: Minimum:
`(0,3)`

`\mathrm{For\:a\:parabola}\:ax^2+bx+c\:\mathrm{with\:Vertex}\:\left(x_v,\:y_v\right)`

`\mathrm{If}\:a < 0\:\mathrm{the\:range\:is}\:f\left(x\right)\le \:y_v`

`\mathrm{If}\:a > 0\:\mathrm{the\:range\:is}\:f\left(x\right)\ge \:y_v`

`a=3,\:\mathrm{Vertex}\:\left(x_v,\:y_v\right)=\left(0,\:3\right)`

`f\left(x\right)\ge \:3`