Question

In Desmos, type in y= square root of x ; y= x² in the graph

the domain of square root of x [0, infinity) and the range is [0, infinity)

the domain of x² is ( - infinity, infinity) and the range is [0, infinity)

What do you notice about the domain/ range of square root of x and x²?

Answer 1

given that :

1). $y=\sqrt{x}$

domain = $[0,\infty)$ and range = $[0,\infty)$

2). $y=x^2$

domain = $(-\infty,+\infty)$ and range = $[0,\infty)$

both graph have different domain but have same range, this is because as in first graph $\sqrt{x}$ is present which is taken only the positive values of x for obtaining the real values range of graph. Thus, the domain of this graph is $[0,\infty)$ and gives values as range is $[0,\infty)$ .

But in the second graph x² is present and due to square nature it can take all real values either positive or negative as domain but its range is $[0,\infty)$, as all the negative values of the x turn to positive value due to squaring so it doesn't gives negative values.