# Chapter P - P.1 - Graphs and Models - Exercises: 51

The intercept with $y$ axis is $y=6$. There are two intercepts with $x$ axi: $x=6$ and $x=-6$. The graph is symmetric and shown on the figure.

#### Work Step by Step

To find the intercept with $y$ axis put $x=0$ and solve for $y$: $$y=6-|0| = 6-0 = 6.$$ To find the intercept with $x$ axis put $y = 0$ and solve for $x$: $$0=6-|x|.$$ Put $|x|$ to the left side to get $$|x| = 6.$$ This is possible for two values of $x$: $$x=-6\text{ and } x=6$$ because the absolute value notation "removes" the minus sign from the number if it's there. To test the symmetry we put $-x$ instead of $x$: $$y(-x) = 6-|-x| = 6-|x| = y(x)$$ where we used the fact that $|x| = |-x|$ for every number $x$ because the absolute value would just "eat" the minus sign if it appears in front of a number inside the $||$ brackets. Since $y(x)=y(-x)$ the graph is symmetric.

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