  We investigate the shadow, deflection angle, and the greybody bounding of a
Schwarzschild-AdS/dS black hole in scale-dependent gravity. We used the EHT
data to constrain the parameter $\epsilon$. We have found that within the
$1\sigma$ level of uncertainty, $\epsilon M_0$ ranges at $10^{-11} - 10^{-16}$
orders of magnitude for Sgr. A*, and $10^{-11} - 10^{-17}$ for M87*. Using
these parameters, we explored how the shadow radius behaves as perceived by a
static observer. Using the known parameters for Sgr. A* and M87*, we found
different shadow cast behavior near the cosmological horizon even if the same
scaling parameters were used. We explored the deflection angle $\hat{\alpha}$
in the weak field limit for both massive and null particles, in addition to the
effect of finite distances using the non-asymptotically flat version of the
Gauss-Bonnet theorem. We have found that the $\hat{\alpha}$ strongly depends on
massive particles. Tests on $\epsilon$'s effect using Sgr. A* is only along
points of low impact parameters. For M87*, only the scaled BH in AdS type can
be tested at high impact parameters at the expense of very low value for
$\hat{\alpha}$. We study the rigorous bound on the greybody factor for scalar
field emitted from black holes in the theory and show the bound on the
transmission probability. The effects of the scale-dependent gravity on the
greybody factors are investigated, and the results indicate that the bound on
the greybody factor in this case is less than the bound for the Schwarzschild
black hole.
