Answer:
2nd choice (see below)
Step-by-step explanation:
The base of the logarithm is 1/5, so the logs of larger numbers will be more and more negative. 3 is subtracted from the logarithm.
A couple of points on the curve are ...
[tex]f(1)=\log_{\frac{1}{5}}{(1)}-3=0-3=-3 \qquad\text{point (1,-3)}[/tex]
This point is on curves B and D.
Another point is ...
[tex]f(5)=\log_{\frac{1}{5}}{(5)}-3=-1-3=-4 \qquad\text{point (5,-4)}[/tex]
This point is on curve B.
_____
If your graphing calculator cannot handle fractional bases, you can use the change of base formula to rewrite the function as ...
f(x) = log(x)/log(1/5) -3 ≈ -1.43067656·log(x) -3
Note that the multiplier is negative, so the function value will head toward +∞ as x→0.
