Chapter 6.3, Problem 41PPS

To determine

The square root function represented by the graph.

Answer to Problem 41PPS

  $y=\sqrt{x-4}-6$

Explanation of Solution

Given:

The graph is :

  

Calculation:

From the graph , the origin of the graph is (4,-6).

So , it is the graph of $y=\sqrt{x}$ shifted 4 units to the right on x-axis and 6 units down on the y-axis.

Its domain is all real numbers greater than or equal to 4.

So, due to the domain of the function , or since it is moved 4 units on the positive side of x-axis , we have:

  $\sqrt{x-4}$

and due to its shift on the negative y-axis by 6 units , we have the final function:

  $y=\sqrt{x-4}-6$