# How do you graph the inequality y<sqrt(x+3)+5?

Nov 16, 2016

#### Explanation:

The reason for the graph looking like this, is because $y = \sqrt{x}$ is a parabola on its side, but in order for this to be a function, the values for the range can only be positive. All you do from here, are the horizontal and vertical shifts ($y = \sqrt{x + h} + k$). ($- h , k$) are the coordinates of the new vertex. the $h$ is the horizontal shift ($- 3$) and the $k$ is the vertical shift ($5$)

Nov 16, 2016

First graph the equality. Then, pick any point on either side of that curve and calculate whether it satisfies the inequality.

#### Explanation:

First graph the equality. That curve is the boundary, it should be “dotted”, not continuous because it is NOT part of the solution.

Then, pick any point on either side of that curve and calculate whether it satisfies the inequality. If it does, then every part of the graph on that side of the curve is part of the solution space. If it does not, then the other side is the solution space.