Answer:
Graph of parent function stretch vertically by factor 2 and shifts 1 units down to get the graph of f(x).
Step-by-step explanation:
The given function is
[tex]f(x)=2x^3-1[/tex]
Its parent function is
[tex]g(x)=x^3[/tex]
The translation is defined as
[tex]f(x)=kg(x+a)+b[/tex] ... (1)
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.
The given function can be written as
[tex]f(x)=2g(x)-1[/tex] ...(2)
On comparing (1) and (2), we get
[tex]k=2,a=0,b=-1[/tex]
It means graph of parent function stretch vertically by factor 2 and shifts 1 units down to get the graph of f(x).
