Question

Find the range of Fac{2}{x-7} " alt="f(x)= \frac{2}{x-7} " align="absmiddle" class="latex-formula">

Answer 1

Answer: $y \in R; y \neq 0$
Explanation: For this, it is often best to find the horizontal asymptote, and then take limits as x approaches the vertical asymptote and the end behaviours.

Well, we know there will be a horizontal asymptote at y = 0, because as x approaches infinite and negative infinite, the graph will shrink down closer and closer to 0, but never touch it. We call this a horizontal asymptote.
So we know that there is a restriction on the y-axis.

Now, since we know the end behaviours, let's find the asymptotic behaviours.

As x  approaches the asymptote of 7⁻, then y would be diverging out to negative infinite.
As x approaches the asymptote at 7⁺, then y would be diverging out to negative infinite.

So, our range would be: $y \in R; y \neq 0$