Question

How does the graph of the function f(x)=2x^3-1 differ from the graph of its parent function?

Answer 1

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

$f(x)=2x^3-1$

Its parent function is  

$g(x)=x^3$

The translation is defined as

$f(x)=kg(x+a)+b$                ... (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  

$f(x)=2g(x)-1$         ...(2)

On comparing (1) and (2), we get

$k=2,a=0,b=-1$

It means graph of parent function stretch vertically by factor 2 and shifts 1 units down to get the graph of f(x).