Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Graphing Radical Functions

Graphing Radical Functions 1.2 - Solution

arrow_back Return to Graphing Radical Functions

We want to match the given radical function with its graph. f(x)=x+2\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. x+20x-2\begin{gathered} x+2\geq 0 \quad \Leftrightarrow \quad x \geq \text{-}2 \end{gathered} Therefore, we will use x-x\text{-}values greater than or equal to -2.\text{-}2. Let's start!

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

The ordered pairs (-2,0),({\color{#0000FF}{\text{-} 2}},{\color{#009600}{0}}), (-1,1),({\color{#0000FF}{\text{-} 1}},{\color{#009600}{1}}), (0,1.414),({\color{#0000FF}{0}},{\color{#009600}{1.414}}), (1,1.732),({\color{#0000FF}{1}},{\color{#009600}{1.732}}), and (2,2)({\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.