Answer
(a) See the image below.
(b) Those graphs are all transformations of $\log(x)$
Work Step by Step
We have a parent function: $f(x) = \log(cx)$. To draw graphs of the family for $c=1, 2, 3, 4$ we will simply input these values and using Graphical Calculator graph them.
(a)
$f(x) = \log(x)$ (Black graph in the image)
$f(x) = \log(2x)$ (Blue graph in the image)
$f(x) = \log(3x)$ (Green graph in the image)
$f(x) = \log(4x)$ (Red graph in the image)
(b) $c$ value in this case means to shrink the parent function graph horizontally by a factor of $c$