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