How do you write $y = |9 - x| +7$ into piecewise functions?

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Answer 1 · 2016-07-11T13:13:59

$y=16-x, if 9>=x,$ and, $y=x-2, x>9.$

Recall that $AA t in RR, |t|=t. if t>=0, and, |t|=-t, if t<0.$

Accordingly, $(i) |9-x|=9-x, if (9-x)>=0, i.e., 9>=x,$ and,
$(ii) |9-x|=-(9-x), if (9-x)<0. or, x>9.$

Therefore, in $(i), y=|9-x|+7=9-x+7=16-x, if, 9>=x$ , whereas,
in $(ii), y=-(9-x)=7=-9+x+7=x-2, if, x>9.$

Altogether, $y=16-x, if 9>=x,$ and, $y=x-2, x>9.$

How do you write y = |9 - x| +7y = |9 - x| +7 into piecewise functions?