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: 52

Answer

The intercept with $y$ axis is $y=6$. The intercept with $x$ axis is $6$. The graph is symmetric with respect to vertical line $x=6$ and is shown on the figure.
1492740731

Work Step by Step

To find the intercept with $y$ axis put $x=0$ and calculate $y$: $$y=|6-0|=|6| = 6.$$ To find the intercept with $x$ axis put $y=0$ and calculate $x$: $$0=|6-x|.$$ The absolute value of something is zero only if that something is equal to zero so we have $$6-x=0$$ or $$x=6.$$ To test the symmetry we will put $-x$ instead of $x$: $$y(-x) = |6-(-x)|= |6+x|.$$ We see that $y(-x) $ is neither equal to $y(x)$ nor $-y(x)$ so this graph is not symmetric. However it is symmetric with respect to the vertical line passing through $x=6$ because when you go, lets say $1$ unit left of $6$ you get $$y=|6-5|=|1|=1$$ and if you go $1$ unit to the right of $6$ you again obtain $$y=|6-7| = |-1|= 1.$$ So if you go the same distance to the left of to the right of $6$ you will calculate the same value for $y$ indicating the symmetry.
Small 1492740731
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.