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

1 Answer
Jul 11, 2016

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

Explanation:

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.