Stitz-Zeager_College_Algebra_e-book

Determine which of the following equations represent

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Unformatted text preview: this equation. Hence, this equation does not represent y as a function of x. 2. x2 + y 3 y3 3 y3 y For every choice of x, the equation y = equation describes y as a function of x. = = = = √ 3 1 1 − x2 √ 3 1 − x2 √ 3 1 − x2 1 − x2 returns only one value of y . Hence, this 3. x2 y = 1 − 3y + 3y = 1 2+3 yx =1 1 y= 2+3 x x2 y factor For each choice of x, there is only one value for y , so this equation describes y as a function of x. Of course, we could always use our graphing calculator to verify our responses to the previous example. For example, if we wanted to verify that the first equation does not represent y as a function of x, we could enter the equation for y into the calculator as indicated below and graph. Note that we need to enter both solutions − the positive and the negative square root − for y . The resulting graph clearly fails the Vertical Line Test, so does not represent y as a function of x. 40 Relations and Functions 1.4.1 Exercises 1. Determine which of the following relations represent y...
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