# Make a complete graph of f(x) = \frac{x^2}{x+3}

## Question:

Make a complete graph of {eq}f(x) = \frac{x^2}{x+3} {/eq}

## Make a Complete Graph of {eq}f(x) = \frac{x^2}{x+3} {/eq}

We just have to come up with a graph that shows the most important parts of the graph.

Evidently the whole of {eq}\mathbb{R} {/eq} cannot be drawn.

Some points of the graph could be worked out manually or just have it done by a computer.

What is peculiar about this function.

1. The domain is all real numbers except x=-3

2. for {eq}|x| \to \infty {/eq} the function behaves like f(x)=x.

It might not have been asked for, however an investigation of the function will help.

## Answer and Explanation:

Given function:

{eq}f(x) = \frac{x^2}{x+3} \\ {/eq}

{eq}\quad f(x) = 0 \\ \Rightarrow \frac{x^2}{x+3} = 0 \\ \iff x^2 = 0 \\ \iff x = 0 {/eq}

...

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#### Learn more about this topic:

Graphing Rational Functions That Have Polynomials of Various Degrees: Steps & Examples

from Math 105: Precalculus Algebra

Chapter 4 / Lesson 8
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