Answer:
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
[tex]q(x)=2p(x+3)-6[/tex] ...(1)
The translation is defined as
[tex]q(x)=kp(x+a)+b[/tex] .... (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).
