Precalc0101to0102-page25

Precalc0101to0102-page25 - x 2 + y 2 = 9 does not describe...

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(Section 1.2: Graphs of Functions) 1.2.5 Example 2 (An Equation that Does Not Describe a Function) Show that the equation x 2 + y 2 = 9 does not describe y as a function of x . § Solution (Method 1: VLT) The circular graph of x 2 + y 2 = 9 below fails the VLT, because there exists a vertical line that intersects the graph more than once . For example, we can take the red line ( x = 2 ) below: Therefore,
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Unformatted text preview: x 2 + y 2 = 9 does not describe y as a function of x . Solution (Method 2: Solve for y) This is also evident if we solve x 2 + y 2 = 9 for y : x 2 + y 2 = 9 y 2 = 9 x 2 y = 9 x 2 Any input value for x in the interval 3, 3 ( ) yields two different y outputs. For example, x = 2 yields the outputs y = 5 and y = 5 ....
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