What is the domain and range of $y = (x + 2) /( x + 5)$ ?

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Answer 1 · 2018-06-18T12:58:00

The domain is $x in (-oo,-5) uu(-5,+oo)$ . The range is $y in (-oo,1)uu(1,+oo)$

The denominator must be $!=0$

Therefore,

$x+5!=0$

$=>$ , $x!=-5$

The domain is $x in (-oo,-5) uu(-5,+oo)$

To find the range, proceed as follows :

$y=(x+2)/(x+5)$

$=>$ , $y(x+5)=x+2$

$=>$ , $yx+5y=x+2$

$=>$ , $yx-x=2-5y$

$=>$ , $x(y-1)=2-5y$

$=>$ , $x=(2-5y)/(y-1)$

The denominator must be $!=0$

Therefore,

$y-1!=0$

$=>$ , $y!=1$

The range is $y in (-oo,1)uu(1,+oo)$

graph{(x+2)/(x+5) [-26.77, 13.77, -10.63, 9.65]}

What is the domain and range of y = (x + 2) /( x + 5)y = (x + 2) /( x + 5)?