# How do you graph y=sqrt(x+5), compare it to the parent graph and what is the domain and range?

Feb 25, 2018

Domain $x \in \left[- 5 , + \infty\right)$
Range $y \in \left[o , + \infty\right)$

#### Explanation:

Assumption: The parent graph is $y = \sqrt{x}$

Although 'true' square root is $\pm$ it is not stated as such in the question. We only have + so this is what is called the principle square root. The condition $\pm$ produces the shape $\subset$ so as we only have the positive half of the condition $\pm$ we end up with only the top half of the shape $\subset$

For the value to NOT go into the complex number set of values the 'content' of the root must not become negative.

Thus the minimum value is such that $x + 5 = 0 \implies x = - 5$.

The 'action' of changing $y = \sqrt{x} \text{ to } y = \sqrt{x + 5}$ 'moves' the graph of $y = \sqrt{x}$ to the left on the x-axis by 5.

The x-intercept is at $y = 0 = \sqrt{x + 5}$ thus ${x}_{\text{intercept}} = - 5$
The y-intercept is at $x = 0 \implies y = \sqrt{5} \approx 2.24$ to 2dp
Domain $x \in \left[- 5 , + \infty\right)$
Range $y \in \left[o , + \infty\right)$