Graphing Radical Functions

We want to match the given radical function with its graph. $\begin{gathered} f(x)=\sqrt{x+2} \end{gathered}$ To do so, we will start by making a table of values. Recall that the radicand cannot be negative. $\begin{gathered} x+2\geq 0 \quad \Leftrightarrow \quad x \geq \text{-}2 \end{gathered}$ Therefore, we will use $x\text{-}$ values greater than or equal to $\text{-}2.$ Let's start!

$x$	$\sqrt{x+2}$	$f(x)=\sqrt{x+2}$
${\color{#0000FF}{\text{-} 2}}$	$\sqrt{{\color{#0000FF}{\text{-}2}}+2}$	${\color{#009600}{0}}$
${\color{#0000FF}{\text{-} 1}}$	$\sqrt{{\color{#0000FF}{\text{-}1}}+2}$	${\color{#009600}{1}}$
${\color{#0000FF}{0}}$	$\sqrt{{\color{#0000FF}{0}}+2}$	${\color{#009600}{1.41421\dots}}$
${\color{#0000FF}{1}}$	$\sqrt{{\color{#0000FF}{1}}+2}$	${\color{#009600}{1.73205\dots}}$
${\color{#0000FF}{2}}$	$\sqrt{{\color{#0000FF}{2}}+2}$	${\color{#009600}{2}}$

The ordered pairs $({\color{#0000FF}{\text{-} 2}},{\color{#009600}{0}}),$ $({\color{#0000FF}{\text{-} 1}},{\color{#009600}{1}}),$ $({\color{#0000FF}{0}},{\color{#009600}{1.414}}),$ $({\color{#0000FF}{1}},{\color{#009600}{1.732}}),$ and $({\color{#0000FF}{2}},{\color{#009600}{2}})$ all lie on the graph of the function. Now, we will plot and connect these points with a smooth curve.

As we can see, the graph of the function is given in choice A.

Graphing Radical Functions 1.2 - Solution