# How do you graph y=sqrt(x-1.5), compare it to the parent graph and what is the domain and range?

Jan 13, 2018

See explanation.

#### Explanation:

the parent function for $g \left(x\right) = \sqrt{x - 1.5}$ is $f \left(x\right) = \sqrt{x}$.

The domain and range of the parent function are $x \ge 0$ and $y \ge 0$, respectively.

$g \left(x\right)$ is a shift of the parent function 1.5 units to the right. This does not change the range of the function but changes the domain to $x \ge 1.5$. The shape of the curve is exactly the same.