How do you find the domain and range of #f(x)=(x^2-x)/(x+1)#?
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"If the momentum of an object increases by #20%#, what will be the percent increase in its kinetic energy?"
Before we do anything, let's see if we can simplify the function by factoring the numerator and denominator.
#(x^2-x)/(x+1)#
#((x)(x-1))/(x+1)#
The domain of a function is all of the #x#values (horizontal axis) that will give you a valid y-value (vertical axis) output.
Since the function given is a fraction, dividing by #0# will not yield a valid #y# value. To find the domain, let's set the denominator equal to zero and solve for #x#. The value(s) found will be excluded from the range of the function.
#x+1=0#
#x=-1#
So, the domain is all real numbers EXCEPT #-1#. In set notation, the domain would be written as follows:
#(-oo,-1)uu(-1,oo)#
The range of a function is all of the #y#-values that it can take on. Let's graph the function and see what the range is.
graph{(x^2-x)/(x+1) [-10, 10, -5, 5]}
