How do you graph y=1/2sqrtx, compare it to the parent graph and what is the domain and range?

Oct 22, 2017

The graph of $y$ is the standard graph $f \left(x\right) = \sqrt{x}$ scaled by $\frac{1}{2}$
Domain: $\left[0 , + \infty\right)$ Range: $\left[0 , + \infty\right)$

Explanation:

The graph of $y$ is the standard graph $f \left(x\right) = \sqrt{x}$ scaled by $\frac{1}{2}$

The graphs of $y$ (lower) and $\sqrt{x}$ (upper) are shown below.

graph{(1/2sqrt(x)-y)(sqrt(x)-y)=0 [-2.653, 9.833, -3.12, 3.125]}

$y$ is defined $\forall x \in \mathbb{R} \ge 0$

Hence the domain of $y$ is $\left[0 , + \infty\right)$

$y = 0$ at $x = 0$

$y$ has no finite upper bound.

Hence the range of $y$ is also $\left[0 , + \infty\right)$