We will first graph the given square root function. Then, we will compare the graph to the graph of its parent function.

Graph

Before we draw the graph of the square root function, we need to first determine the domain of our function. To find the domain of

q (x) = x + 8,

recall that the radicand of a square root is always greater than or equal to

0 .

x \geq 0

Therefore, the domain of the given function is all real numbers greater than or equal to

0 .

With this in mind, we will make a table of values to graph the function.

$x$	$x + 8$	$q (x) = x + 8$
$0$	$0 + 8$	$8$
$4$	$4 + 8$	$10$
$16$	$16 + 8$	$12$
$36$	$36 + 8$	$14$

Let's plot and connect the obtained points. Remember, the domain is all real numbers greater than or equal to $0,$ so we do not want to extend the function any farther to the left.

Comparison With the Parent Function

To compare the graph of our function with the graph of the parent function $f (x) = x,$ we will consider some possible transformations.

Vertical Translations
$Translation up k units, k > 0 y = f (x) + k$	$Translation down k units, k > 0 y = f (x) - k$

Let's now identify the transformations in our function.

q (x) = x + 8

The graph of the given function is a vertical translation up by

8

units of the graph of

f (x) = x .

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