I am totally lost on this question...any kind of help would be very appreciated!

y = 9 * (1/5)^x
take the logarithm
log y = log 9 + x*log (1/5)
since log(1/5) is a negative number, as x increases in postive direction, log y decreases
in fact, log y will go all the way to inf as x goes to +inf (inf = infinity)
but the antilog of log y = inf is y = zero.
so y > 0, or zero is the horizontal asymptote
take the logarithm
log y = log 9 + x*log (1/5)
since log(1/5) is a negative number, as x increases in postive direction, log y decreases
in fact, log y will go all the way to inf as x goes to +inf (inf = infinity)
but the antilog of log y = inf is y = zero.
so y > 0, or zero is the horizontal asymptote