# How do you graph y=-1/4sqrtx, compare it to the parent graph and what is the domain and range?

Nov 1, 2017

$y$ is the standard graph of $f \left(x\right) = \sqrt{x}$ scaled by $- \frac{1}{4}$
Domain: $\left[0 , + \infty\right)$ Range: $\left[0 , - \infty\right)$

#### Explanation:

$y = - \frac{1}{4} \sqrt{x}$

$y$ is the standard graph of $f \left(x\right) = \sqrt{x}$ scaled by $- \frac{1}{4}$

We can see the graphs of $y$ (Lower) and $\sqrt{x}$ (Upper) below.

graph{(y+1/4sqrtx)(y-sqrtx)=0 [-3.84, 18.66, -5.535, 5.705]}

As can be deduced from the graph of $y$ above:

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

$y$ has no finite lower bound.

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