Chapter EP, Problem 7.3.17EP

To determine

To graph: The inequality $y\ge \sqrt{8x-3}+1$ .

Explanation of Solution

Given information:

The square root inequality $y\ge \sqrt{8x-3}+1$ .

Graph:

First graph the boundary of the inequality that is $y=\sqrt{8x-3}+1$ .

Since, the inequality is greater than or equal to so the line will be solid.

Also the square root function does not accept negative value, so domain is $\left\{x|x\ge \frac{3}{8}\right\}$ .

Observe that y is greater than or equal therefore the shaded region will lie above the boundary and within the range. It will also include points of boundary.

Interpretation:

The region represented by the inequality is unbounded. As the value of x increases the corresponding values of y increases.