Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.9 - The Coordinate Plane; Graphs of Equations; Circles - 1.9 Exercises - Page 104: 81

Answer

$(a)$ See the image below $(b)$ $x$-intercept doesn't exist $y$-intercepts - $B(0,-2)$ $(c)$ Solving the equation gives us the following: $x$-intercept never happens For $y$ intercept: $x=0$ ; $y=-2$

Work Step by Step

$(a)$ We simply input the equation and get the graph. See the image above. $(b)$ As we clearly see from the graph, we have no $x$-intercept (The graph approaches $x$-axis but never cross it) $y$-intercepts - $B(0,-2)$ $(c)$ $y=-\frac{2}{x^2+1}$ For $x$-intercept, we need to find $x$ values where $y=0$ $-\frac{2}{x^2+1}=0$ It will never get $0$ as denominator cannot be $0$. $x$-intercept doesn't exist. For $y$-intercept, we need to find $y$ values where $x=0$ $y=-\frac{2}{0^2+1}=-\frac{2}{1}=-2$
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