Determine if the equation $x ^ { 2 } + ( y - 1 ) ^ { 2 } = 36$ defines y as a function of x
A) The equation represents a function because it's a circle
B) The equation represents a function because for each value of x there is always two values of y
C) Not a function because the equation gives two values of y for a given value of x
D) The equation represents a function because it passes the vertical line test
E) Not a function because the equation passes the vertical line test.

Question

Quizplus · Accepted Answer

The equation $x^2 + (y-1)^2 = 36$ represents a circle with center at (0,1) and radius 6. For most values of x within the domain of the circle, there are two corresponding values of y (one above the center and one below). This violates the definition of a function, which requires that each input (x) maps to exactly one output (y).

Determine If the Equation x2+(y−1)2=36x ^ { 2 } + ( y - 1 ) ^ { 2 } = 36x2+(y−1)2=36

Determine If the Equation $x ^ { 2 } + ( y - 1 ) ^ { 2 } = 36$