How does replacing f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative) affect the graph?

F(x) + k - Moves the graph k units up.

k f(x)   stretches the graph parallel to y-axis by a facor k

f (kx) stretches  the  graph by a factor 1/k parallel to x-axis

f(x + k)  moves the graph   3 units to the left.

For k negative the first one moves it k units down

for second transform negative does same transfoormation but also reflects the graph in the x axis

For the third transform negative k :- same as above but also reflects in y axis

4th transform -  negative k moves graph k units to the right