Question

What is the range of the function y = x 2?

Answer 1

`\mathrm{Range\:of\:}x^2:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}`

The graph is also attached below.

Explanation:

Given the function

`y=x^2`

• We know that the range of a function is the set of values of the dependent variable for which a function is defined.

`\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=1,\:\mathrm{Vertex}\:\left(x_v,\:y_v\right)=\left(0,\:0\right)`

`f\left(x\right)\ge \:0`

Thus,

`\mathrm{Range\:of\:}x^2:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}`

The graph is also attached below.