Question

graph the function $f(x) = -3\log_{2}(-x - 4) - 8$ on the axes below. you must plot the asymptote and any two points with integer coordinates.
asymptote:
vertical
horizontal

Explanation:

Step1: Find vertical asymptote

Set argument of log to 0:
$-x - 4 = 0$
Solve for $x$:
$x = -4$
Logarithmic functions have vertical asymptotes, so this is a vertical asymptote.

Step2: Find first integer point

Choose $x=-5$ (integer < -4):
$f(-5) = -3\log_2(-(-5)-4)-8 = -3\log_2(1)-8$
Since $\log_2(1)=0$,
$f(-5) = -3(0)-8 = -8$
Point: $(-5, -8)$

Step3: Find second integer point

Choose $x=-6$ (integer < -4):
$f(-6) = -3\log_2(-(-6)-4)-8 = -3\log_2(2)-8$
Since $\log_2(2)=1$,
$f(-6) = -3(1)-8 = -11$
Point: $(-6, -11)$

Answer:

Asymptote: Vertical, $x=-4$
Points to plot: $(-5, -8)$ and $(-6, -11)$