Q3:      Sketch the graph of  for the function f with given graph (shown in red in the answers below).

 

 

A3:

 

Since what we know is the effect of replacing x by either cx or x+c, our goal is to describe the replacement of x  by 2x+1 as two such steps.

 

But if we first replace x by 2x to get the squashed graph , then replacing the x here by x+1 gives , which is not what we want. To get  we need to replace the x in  with just , so a correct sequence is squash by 2 then shift left by half  as shown in the graph on the left below.

 

     

 

On the other hand, we can also get from x to 2x+1  if we first replace  x  by x+1  (shifting the graph left by one), and then replace x by 2x. So another correct sequence is first shift left by 1 then squash the result  as shown in the graph on the right above.