functions with absolute value

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erinnnxxo

15 septembre 2017 01:12

hello! I just had 2 homework questions that had to do with absolute value.

the first one was finding the domain and range of f(x)=|x|/x but instead of a getting a piecewise function graph, it got a greatest integer function graph (step graph). I thought all absolute value gave the graph a v shape? also I'm confused how to plug number into this graph if someone could give me and example id appreciate it (:

secondly, I had another question that was f(x)=x+6/|x+6| and it asked for the domain and range. how do I plug numbers into this equation if the bottom is absolute value? if I do the same thing on top and bottom it would give me things like 6/6 or 7/7 which would always equal one.

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Kuan Yi Ng

7 octobre 2017 23:35
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1. f(x)=|x|/x

from |x| we know that, f(x) will switch between (+) and (-) at x = 0

for example,

when x = 1 , f(1) = |1| / 1 = 1

when x = -1 f(-1) = |-1| / (-1) = -1

2. f(x)=x+6/|x+6|

this will be quite simliar to the above example, the difference will be the value of x at which f(x) switches between (+) and (-)

*reference

https://www.khanacademy.org/math/algebra-home/alg-absolute-value

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functions with absolute value

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