FUNCTION HELP PLEASE

Question

How can you tell if a function has been translate vertically versus horizontally?

How can you tell if a function has been translate vertically stretched versus horizontally stretched?

How can you tell if a function has been translate vertically compressed versus horizontally compressed?

Wanted to know it was represented mathematically, like f(x) = x then vertical translation would be....

Answer 1

if the original function is y = f(x), then

 

   (a)  if y = f(x) + k;   translate vertically upward, if k > 0; translate vertically downward if k <0

 

   (b)  if y = f(x-a);  translate horizontally to the right, if a > 0;  translate horizontally to the left, if a < 0

 

   (c)  if y = af(x);  if a > 1, then stretch vertically, or (alternatively) compress horizontally

                            if a < 1, then stretch horizontally, or (alternatively) compress vertically