# F(x)=x+8/x+6 how you slove this problem?

## f(x)=x+8/x+6

See below:

#### Explanation:

We have:

$f \left(x\right) = \frac{x + 8}{x + 6}$

Let's first see that when $x = - 6$, the denominator $= 0$ which will make the fraction undefined.

When values of $x$ approach $- 6$ from the right (meaning the denominator gets smaller and smaller but remains positive), the fraction will start to approach positive infinity (both numerator and denominator will be positive).

When values of $x$ approach $- 6$ from the left (meaning the denominator gets smaller and smaller but remains negative), the fraction will start to approach negative infinity (the numerator will be positive but the denominator negative).

We can also see that when $x = - 8$, the numerator $= 0$ which will make the value of the fraction 0.

And as $x$ approaches both positive and negative infinity, we'll in effect be saying $\frac{\infty}{\infty}$ and $\frac{- \infty}{- \infty}$, both of which are equal to 1.

Let's do a brief table (where ${6}^{+}$ refers to approaching 6 from the right and ${6}^{-}$ refers to approaching 6 from the left):

$\left(\begin{matrix}x & y \\ - \infty & 1 \\ \infty & 1 \\ - 8 & 0 \\ - 6 & \text{undef} \\ - {6}^{+} & \infty \\ - {6}^{-} & - \infty\end{matrix}\right)$

And the graph looks like this:

graph{(x+8)/(x+6) [-16.29, 3.71, -7.2, 7.8]}