No. A function is a "graph" the survives the "vertical line test". Namely, it is for every x in its domain, there can be one and only one f(x) in its co-domain. An ellipse clearly fails it at everywhere except it's two vertex.
But an ellipse can be thought as two separate functions. A standard ellipse relation, x^2 / a + (y)^2 / b = 1, can be thought as two separate real functions of y1 and y2. where y1 = -y2 exactly.
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An ellipse is a conic section which is a closed curve. A circle is a special case of an ellipse.
Yes. It's the graph of [ Y = f(X) ] described by (X/A)2 + (Y/B)2 = C2 A, B, and C are constants. If 'A' and 'B' are both '1', then the graph is a circle with radius 'C'.
Conics, or conic sections, are the intersection of a plane with an infinite double cone. If that plane cuts both cones, it is a hyperbola. If it is parallel to the edge of the cone, you get a parabola. If neither is the case, it is an ellipse. The ellipse is also a circle if the plane is perpendicular to the altitude of the cone. Note that none of these are the case if the plane passes through the vertex of the cone.
An ellipse is produced.
If y is an exponential function of x then x is a logarithmic function of y - so to change from an exponential function to a logarithmic function, change the subject of the function from one variable to the other.