Question

graph the function $f(x) = -3\log_{4}(-x + 2) + 7$ 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:
$-x + 2 = 0$
Solve for $x$:
$x = 2$
Logarithmic functions have vertical asymptotes, so this is a vertical asymptote at $x=2$.

Step2: Find first integer point

Choose $x=1$ (integer less than 2):
$f(1) = -3\log_4(-1 + 2) + 7 = -3\log_4(1) + 7$
Since $\log_4(1)=0$,
$f(1) = -3(0) + 7 = 7$
Point: $(1, 7)$

Step3: Find second integer point

Choose $x=-2$ (integer less than 2):
$f(-2) = -3\log_4(-(-2) + 2) + 7 = -3\log_4(4) + 7$
Since $\log_4(4)=1$,
$f(-2) = -3(1) + 7 = 4$
Point: $(-2, 4)$

Answer:

Asymptote: Vertical, $x=2$
Points to plot: $(1, 7)$ and $(-2, 4)$