Question

graph the function $f(x)=3\log_2(-x - 6)-2$ on the axes below. you must plot the asymptote and any two points with integer coordinates.
asymptote:

Explanation:

Step1: Find the vertical asymptote

For a logarithmic function \(y = \log_b(u)\), the vertical asymptote occurs when \(u = 0\).
For \(f(x)=3\log_2(-x - 6)-2\), set \(-x - 6=0\).
Solving for \(x\):
\(-x-6 = 0\)
\(-x=6\)
\(x=-6\)

Step2: Find two points with integer coordinates

Let's find \(y\) - values for some \(x\) - values.

Point 1: Let \(x=-8\)

$$
LATEXBLOCK0
$$

So, the point is \((-8,1)\)

Point 2: Let \(x=-14\)

$$
LATEXBLOCK1
$$

So, the point is \((-14,7)\)

Answer:

Asymptote: \(x = - 6\), two points are \((-8,1)\) and \((-14,7)\)