For #h(x)=abs[x]#; how do you find h(-4),h(4),and h(-3)?

1 Answer
Stefan V.
Sep 1, 2015

#h(-4) = h(4) = 4#
#h(-3) = 3#

Explanation:

Your function #h(x)# is defined as the absolute value of #x#, written as #|x|#, which will always return a positive values regardless of the sign of #x#.

#color(blue)(|x| = {(x", " "if " x >=0), (-x", " "if "x<0) :})#

So, to find #h(-4)#, simply replace #x# with #(-4)#. Since #(-4)<0#, the absolute value function will return

#h(-4) = |-4| = - (-4) = color(green)(4)#

For #h(4)#, you have #x=4#, and since #4>=0#, the absolute value function will return

#h(4) = |4| = color(green)(4)#

The function returned the same value for both #(-4)# and #4#. For #h(-3)# you have #(-3)<0#, so the function will return

#h(-3) = |-3| = -(-3) = color(green)(3)#

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