Chapter EP, Problem 7.3.18EP

To determine

To graph: The inequality $y<\sqrt{5x-1}+3$ .

Explanation of Solution

Given information:

The square root inequality $y<\sqrt{5x-1}+3$ .

Graph:

First graph the boundary of the inequality that is $y=\sqrt{5x-1}+3$ .

Since, the inequality is strictly less so the line will be dashed.

Also the square root function does not accept negative value, so domain is $\left\{x|x\ge \frac{1}{5}\right\}$ .

Observe that y is less than therefore the shaded region will lie below the boundary and within the range.

Interpretation:

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