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Graphing Radical Functions

Graphing Radical Functions 1.11 - Solution

arrow_back Return to Graphing Radical Functions

Let's graph the function by making a table of values.

xx x+82\sqrt{x+8}-2 f(x)=x+82f(x)=\sqrt{x+8}-2
-8{\color{#0000FF}{\text{-} 8}} -8+82\sqrt{{\color{#0000FF}{\text{-} 8}}+8}-2 -2{\color{#009600}{\text{-} 2}}
-7{\color{#0000FF}{\text{-} 7}} -7+82\sqrt{{\color{#0000FF}{\text{-} 7}}+8}-2 -1{\color{#009600}{\text{-} 1}}
-6{\color{#0000FF}{\text{-} 6}} -6+82\sqrt{{\color{#0000FF}{\text{-} 6}}+8}-2 -0.59\approx {\color{#009600}{\text{-} 0.59}}
-5{\color{#0000FF}{\text{-} 5}} -5+82\sqrt{{\color{#0000FF}{\text{-} 5}}+8}-2 -0.27\approx {\color{#009600}{\text{-} 0.27}}
-4{\color{#0000FF}{\text{-} 4}} -4+82\sqrt{{\color{#0000FF}{\text{-} 4}}+8}-2 0{\color{#009600}{0}}
-3{\color{#0000FF}{\text{-} 3}} -3+82\sqrt{{\color{#0000FF}{\text{-} 3}}+8}-2 0.24\approx {\color{#009600}{0.24}}

Let's now plot the points and connect them with a smooth curve.

Domain

The domain of radical functions only includes values for which the radicand{\color{#FF0000}{\text{radicand}}} is non-negative. f(x)=x+82\begin{gathered} f(x)=\sqrt{{\color{#FF0000}{x+8}}}-2 \end{gathered} We can solve for these values of xx by only looking at the radicand. x+80x-8\begin{gathered} x+8 \geq 0 \quad \Leftrightarrow \quad x \geq \text{-} 8 \end{gathered} The domain is all real numbers greater than or equal to -8.\text{-} 8.

Range

To identify the range, we will draw the graph of the function. We can see that the range is all real numbers greater than or equal to -2.\text{-} 2.

Conclusion

Finally, let's summarize our findings. Domain:  x-8Range:  f(x)-2\begin{aligned} \textbf{Domain:}&\ \ x \geq \text{-} 8 \\ \textbf{Range:}& \ \ f(x) \geq \text{-} 2 \end{aligned}