Chapter 10.1, Problem 15E

To determine

To match the function and describe the range.

Answer to Problem 15E

Option D

Range = $[0,\infty )$

Explanation of Solution

Given information: $y=\sqrt{x-3}$

Formula Used: Square root function cannot be negative.

Calculation:

As the domain of square root function is greater than or equal to zero i.e. cannot be negative.

So,

  $\sqrt{x-3}\ge 0$

Squaring both sides,

  $x-3\ge 0$

So, simplify

  $x\ge 3$

Hence,

Domain = $[3,\infty )$

As,

  $\sqrt{x-3}\ge 0$

Now, $y=\sqrt{x-3}$

  $y\ge 0$

Hence,

Range =

  $[0,\infty )$

The graph D has Domain = $[3,\infty )$ and Range = $[0,\infty )$ . So,

Option D is correct.