Question

Is the equation x2+y2=5 a function

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Answer 1

Not a function

Explanation:

Please use " ^ " to denote exponentiation: x^2+y^2=5

This relation has the form x^2+y^2=r^2, which describes a circle of radius r and center at (0, 0). Draw a circle of any radius and then apply the vertical line test: draw a straight vertical line through the circle and count how many times the line intersects the graph.

If you do this properly you'll find that the vertical line intersects the circle in more than one place (that is, in two places).

This fails the vertical line test and tells us that x^2+y^2=5 does NOT represent a function.