Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson

Chapter 1 - Functions and Their Graphs - Section 1.1 Functions - 1.1 Assess Your Understanding - Page 54: 37

Answer

$\text{$y$is NOT a function of$x$.}$

Work Step by Step

For an equation to be a function: any input $x$ will yield only one output $y$ We start by solving the equation for $y$ Rearranging the equation: $$3y^2=1-2x^2$$ Dividing both sides by $3$: $$y^2=\dfrac{1-2x^2}{3}$$ Taking the square root of both sides: $$y = \pm \sqrt{\dfrac{1-2x^2}{3}}$$ If $x=0$ $$y = \pm \sqrt{\dfrac{1-2(0)^2}{3}} = \pm \dfrac{\sqrt{3}}{3}$$ As there are two different outputs resulting from the same input, the equation isn't a function

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