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: 49


The function has no intercepts. The graph is anti symmetric and shown on the figure

Work Step by Step

Graph intercept with $y$ axis is found putting $x=0$ in the equation so we find $$y=\frac{8}{0}$$ but this is impossible because we can't divide by zero. To find the intercept with $x$ axis we put $y=0$ and we get the equation $$0=\frac{8}{x}\Rightarrow x=\frac{8}{0}$$ and again this is impossible since we cannot divide with zero. This means that the graph does not have any intercepts. To test for symmetry we put $-x$ instead of $x$ and we see that $$y(-x) = \frac{8}{-x} = -\frac{8}{x} = -y(x)$$ so this graph is anti symmetric i.e. the part on the negative side of $x$ axis looks like the one of the positive but upside down.
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