Answer:
The parent function is given below as
[tex]y=x^3[/tex]
From the image below,
The parent function has been transformed by shifting it 2 units up to give the equation of b(x) below
[tex]b(x)=x^3+2[/tex]
The function of a(x) is given below as
The stretch factor of b(x) is =1
The stretch factor of a(x) = 1/3
[tex]\begin{gathered} a(x)=\frac{1}{3}x^3 \\ \frac{b(x)}{a(x)}=\frac{1}{\frac{1}{3}}=\frac{1}{1}\times\frac{3}{1}=3 \end{gathered}[/tex]
By comparing the two functions, based on the stretch factor, we can thereby conclude that
[tex]b(x)=3times\text{ }as\text{ }great[/tex]
Hence,
The THIRD OPTION is the right answer
