SOLUTION: does the function |x|-y=6 define y as a function of x

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Question 1117703: does the function |x|-y=6 define y as a function of x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
By definition, a function f is a rule that assigns to each element x
in its domain exactly+one+element, called f%28x%29, in its range.
you are given the function abs%28x%29-y=6
rearrange it: y=abs%28x%29-6
now find out what are the domain and range of y=+abs%28x%29-6
domain: R (all real numbers) or (-infinity,infinity)
range: { y element R+:+y%3E=-6 } or (-6,infinity)
since each element x in its domain exactly+one+y, y=abs%28x%29-6 is a function
or, simply graph it and use vertical line test:


as you can see, both vertical lines intersect graph in exactly one point