Answer:
[tex]\mathrm{Range\:of\:}x^2:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}[/tex]
The graph is also attached below.
Step-by-step explanation:
Given the function
[tex]y=x^2[/tex]
- We know that the range of a function is the set of values of the dependent variable for which a function is defined.
[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=1,\:\mathrm{Vertex}\:\left(x_v,\:y_v\right)=\left(0,\:0\right)[/tex]
[tex]f\left(x\right)\ge \:0[/tex]
Thus,
[tex]\mathrm{Range\:of\:}x^2:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}[/tex]
The graph is also attached below.
