conic sections as functions

[ree]

Are conic sections functions? I am thinking, "yes" because conic sections are cones which make up parabolas, circles, ellipses, and hyperbolas, all of which contain functions. Am I correct?

 

[stapel]

Are conic sections functions?

What is the definition of "function"?

...conic sections are cones...

Not quite. Conic sections, according to an authoritative reference, are "the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone."

In other words, conic sections are geometric objects, formed by the intersection of two other geometric objects. These objects might be expressible as algebraic relations, and these relations might be functions. But conic sections are neither cones (three-dimensional geometric shapes) nor functions (algebraic relations of a particular type), in and of themselves.

Does the question really ask you whether conic sections "are" functions, or does it ask whether they "can be expressed as" functions? And does it ask whether "all" conics may be expressed as function, or if "any" may be?

Thank you.

Eliz.