Question 1208753
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To find the range of this function, rewrite the function in an equivalent form:<br>
{{{y=x/(x-5)}}}<br>
{{{y=((x-5)+5)/(x-5)}}}<br>
{{{y=(x-5)/(x-5)+5/(x-5)}}}<br>
{{{y=1+5/(x-5)}}}<br>
For the expression {{{5/(x-5)}}}...<br>
The limit as x goes to negative infinity is 0, and the value is always negative<br>
The limit as x goes to positive infinity is 0, and the value is always positive<br>
The limit as x approaches 5 on the left is negative infinity<br>
The limit as x approaches 5 on the right is positive infinity<br>
So the range of the expression {{{5/(x-5)}}} is (-infinity,0) U (0,infinity).<br>
And that means<br>
ANSWER: The range of {{{y=x/(x-5)}}} is (-infinity,1) U (1,infinity)<br>
A graph....<br>
{{{graph(400,400,-10,20,-10,5,x/(x-5))}}}<br>