Write the rule that transforms p(x) into q(x), where q(x)=2p(x+3)−6

The graph of p(x) stretch vertically by factor 2 and shifts 3 units left and 6 units down to get q(x).

Step-by-step explanation:

It is given that p(x) and q(x) are two functions such that

   ...(1)

The translation is defined as

             .... (2)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2) we get

k=2>1, so the graph of p(x) stretch vertically by factor 2.

a=3>0, so the graph of p(x) shifts 3 units left.

b=-6<0, so the graph of p(x) shifts 6 units down.

Therefore, the graph of p(x) stretch vertically by factor 2 and shifts 3 units left and 6 units down to get q(x).