Question 1134050
the function is abs(x-7) / abs(x+5)


abs(x+5) is in the denominator.


the denominator will be 0 when x = -5


therefore there is a vertical asymptote at x = -5


both the numerator and the denominator can only be 0 or positive since both numerator and denominator expression are within the absolute value signs.


this means that the overall function will always be greater than or equal to zero because a positive divided by a positive is always positive.


consequently, all values of the function f(x) / g(x) will be positive except at x = -5 when the function has a vertical asymptote.


the graph of the function is shown below.


first is a near end view.
next is a far end view.


<img src = "http://theo.x10hosting.com/2019/020401.jpg" alt="$$$" >


<img src = "http://theo.x10hosting.com/2019/020402.jpg" alt="$$$" >