Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - P.1 - Graphs and Models - Exercises - Page 8: 56

Answer

There are no intercepts with $y$ axis. The intercept with $x$ axis is in $8/3$. The graph is symmetric with respect to $x$ axis and is shown on the figure
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Work Step by Step

To find the intercept with $y$ axis put $x=0$ and calculate $y$: $$3\times0 - 4y^2=8\Rightarrow -4y^2=8\Rightarrow y^2 = -2.$$ The last equation does not have any real solutions because no real number can be squared to yield a negative number so there are no intercepts with $y$ axis. To find the intercept with $x$ axis put $y=0$ and calculate $x$ $$3x-40^2=8\Rightarrow 3x=8\Rightarrow x=\frac{8}{3}.$$ The graph is symmetric with respect to $x$ axis since if we put $-y$ instead of $y$ we obtain the same equation $$3x-4(-y)^2 = 3x-4y^2 = 8$$
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