Question

x + 6Identify the vertical asymptotes of f(x)(1 point)- 9x + 18O x= -6 and x = -3O x= -6 and x = 3oO x = 6 and x = -3O x = 6 and x = 3

Answer 1

So we want to find the vertical asymptotes of the function:

`f(x)=(x+6)/(x^2-9x+18)`

Remember that there's a vertical asymptote at points of x where the denominator of the rational function is 0.

So, equal the denominator to zero:

`x^2-9x+18=0`

And solve this equation for x as follows:

We could factor

`\begin{gathered} x^2-9x+18=0 \\ (x-6)(x-3)=0 \end{gathered}`

Now, notice that any of both factors could be zero, so:

`\begin{cases}x-6=0\to x=6 \\ x-3=0\to x=3\end{cases}`

Therefore, the function has vertical asymptotes at x=6 and x=3.