What is the range of $y=(-4x-3)/(x-2)$ ?

Question

1568 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-04T22:54:25

$f(x) = y = (-4x-3)/(x-2)$

$= ((-4x+8)-11)/(x-2)$

$= (-4(x-2)-11)/(x-2)$

$= -4-11/(x-2)$

$f(x)$ can take any value except $-4$ (to which $f(x)$ is asymptotic as $x -> +- oo$ ).

So the range is $RR$ \ ${-4}$

or in interval notation: $(-oo, -4) uu (-4, oo)$

graph{(-4x-3)/(x-2) [-39.76, 39.8, -19.92, 19.83]}

More explicitly, we can express $x$ in terms of $y$ as

$x = 2-11/(y+4)$

which has an obvious excluded value at $y=4$

What is the range of y=(-4x-3)/(x-2)y=(-4x-3)/(x-2)?