Exercise 44 Page 625

Since we have an absolute value equation we will consider two cases — the negative case and the positive case. Note that the function $y$ is defined in the first and forth quadrants where $x>0,$ $y>0$ and $x>0,$ $y<0,$ respectively. We can now write a piecewise-defined function to describe the graph of $y^2=x$ in the first and forth quadrants.

$x$	$y=\sqrt{x}$	$y$
$0$	$\sqrt{0}$	$0$
$1$	$\sqrt{1}$	$1$
$4$	$\sqrt{4}$	$2$

Now, we will plot these points on the same coordinate system as Part A and connect them with a smooth curve.

We will apply the same procedure to graph the function $y=\text{-}\sqrt{x}.$ Let's make a table of values.

$x$	$y=\text{-}\sqrt{x}$	$y$
$0$	$\text{-}\sqrt{0}$	$0$
$1$	$\text{-}\sqrt{1}$	$\text{-}1$
$4$	$\text{-}\sqrt{4}$	$\text{-}2$

Let's plot these points on the same coordinate system and draw a smooth curve connecting them.

$x$	$y=x$	$y$
$\text{-}1$	$\text{-}1$	$\text{-}1$
$0$	$0$	$0$
$1$	$1$	$1$

Let's draw the line passing through these points.

Now let's plot the points $(2,4),$ $(4,2),$ and $(1,1).$