Respuesta :
[tex]\mathrm{Range\:of\:}3x^2+3:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:3\:\\ \:\mathrm{Interval\:Notation:}&\:[3,\:\infty \:)\end{bmatrix}[/tex]
Function range definition:
- The set of values of the dependent variable for which a function is defined.
Vertex of [tex]3x^{2} +3[/tex]: Minimum: [tex](0,3)[/tex]
[tex]\mathrm{For\:a\:parabola}\:ax^2+bx+c\:\mathrm{with\:Vertex}\:\left(x_v,\:y_v\right)[/tex]
[tex]\mathrm{If}\:a < 0\:\mathrm{the\:range\:is}\:f\left(x\right)\le \:y_v[/tex]
[tex]\mathrm{If}\:a > 0\:\mathrm{the\:range\:is}\:f\left(x\right)\ge \:y_v[/tex]
[tex]a=3,\:\mathrm{Vertex}\:\left(x_v,\:y_v\right)=\left(0,\:3\right)[/tex]
[tex]f\left(x\right)\ge \:3[/tex]
Answer:
[tex][3,\infty)[/tex]
Step-by-step explanation:
[tex]f(x)=3x^2+3\\\\f(x)=3(x-0)^2+3[/tex]
[tex]\{y|y\geq3\}\:\text{or} [3,\infty)[/tex]
