Does the equation $x^{2} + y = 169$ $x^2 +y= 169$ define y as a function of x?

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Answer 1 · 2018-07-12T00:44:01

Yes

Given: $x^{2} + y = 169$ $x^2 + y = 169$

This function can be rearranged to be: $y = 169 - x^{2}$ $y = 169 - x^2$ or $y = - x^{2} + 169$ $y = -x^2 + 169$

This is a quadratic(squared) equation, which is a parabola.

A parabola is a function of $x$ $x$ since it passes the vertical line test:

Each $x$ $x$ value only maps to one $y$ $y$ value.

graph{169-x^2 [-10, 10, -20, 200]}

Does the equation x2+y=169x^2 +y= 169 define y as a function of x?