# How do you find the domain and range of y=sqrt(2x+7)?

Mar 3, 2018

The main driving force here is we can't take the square root of a negative number in the real number system.

#### Explanation:

So, we need to find the smallest number that we can take the square root of that is still in the real number system, which of course is zero.

So, we need to solve the equation $2 x + 7 = 0$

Obviously this is $x = - \frac{7}{2}$

So, that is the smallest, legal x value, which is the lower limit of your domain. There is no maximum x value, so the upper limit of your domain is positive infinity.

So $D = \left[- \frac{7}{2} , + \infty\right)$

The minimum value for your range will be zero, since $\sqrt{0}$ =0

There is no max value for your range, so $R = \left[0 , + \infty\right)$