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: 66


From the graph we see that the points of intersection are $(1,5)$ and $(3,3)$. See step-by-step solution for analytical check.

Work Step by Step

We read from the graph the points of intersection $(1,5)$ and $(3,3)$ ($x$ coordinate is cited 1st, and $y$ coordinate is cited second). To analytically check them we have to substitute $x$ and $y$ from each point (one point by one) to the equations of the graphs and see if they become valid equalities (if number calculated on the right side simply equals the number calculated on the left): For $(1,5)$ $$5=-|2\times 1 - 3|+6 = -|-1|+6 = -1+6=5$$ which is correct. $$5=6-1=5$$ which is also correct so the point $(1,5)$ is analytically verified. For $(3,3)$ $$3=-|2\times3 - 3|+6 = -|6-3|+6 = -|3|+6 = -3+6 = 3$$ which is correct. $$3=6-3=3$$ which is also correct so the point $(3,3)$ is also analytically verified.
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