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

1 Answer
Ratnaker Mehta
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.#

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