SOLUTION: Hi I need some help with evaluating this function. f(x)=abs(x)/x; f(-2),f(-1),f(0),f(5),f(x^2),f(1/x)

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Question 125353: Hi I need some help with evaluating this function.
f(x)=abs(x)/x;
f(-2),f(-1),f(0),f(5),f(x^2),f(1/x)
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
If x is negative, |x|=-x
If x is zero or positive, |x|=x

f%28x%29=abs%28x%29%2Fx
So,
f%28-2%29=abs%282%29%2F-2=2%2F-2=-1
f%28-1%29=abs%28-1%29%2F-1=1%2F-2=-1
f%280%29=abs%280%29%2F0=0%2F0-----this is undefined.
Evidence?
graph%281000%2C1000%2C-20%2C20%2C-20%2C20%2Cabs%28x%29%2Fx%29
There is a discontinuity at x=0.
f%285%29=abs%285%29%2F5=5%2F5=1
Please take note that if x is a real number then x^2 is always positive.
So,
f%28x%5E2%29=abs%28x%5E2%29%2Fx%5E2=x%5E2%2Fx%5E2=1
IF x is positive, 1/x is positive
If x is zero, 1/x is undefined
If x is negative, 1/x is negative
So,
If x is negative,
f%281%2Fx%29=abs%281%2Fx%29%2F%281%2Fx%29=%28-1%2Fx%29%2F%281%2Fx%29=-1
If x is zero,
f%281%2F0%29-----you can see the result, it is undefined
If x is positive,
f%281%2Fx%29=abs%281%2Fx%29%2F%281%2Fx%29=%281%2Fx%29%2F%281%2Fx%29=1

Please watch our video http://www.metacafe.com/watch/1101445/science_avenue/

Power up,
HyperBrain!