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Draw a rough picture of the following surface and also clarify some basic geometric properties...

Question:

Draw a rough picture of the following surface and also clarify some basic geometric properties (e.g. axis, vertex): {eq}x^2 + z^2 = 4 {/eq}.

Graph the functions

We can graph a function in the Cartesian plane or coordinate system when the function is of a variable. The behavior can be seen in the graph, we can also see the geometric properties.

Answer and Explanation:

We have, {eq}x^2 + z^2 = 4 \\ z^2=4-x^{2} \\ z=f(x)= \sqrt{ 2-x^{2} } \\ {/eq}

Graph the function {eq}f(x)= \sqrt{ 2-x^{2} } \\ {/eq}

The function has the geometric shape of a semicircle


Learn more about this topic:

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

from Math 105: Precalculus Algebra

Chapter 4 / Lesson 8
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