Answer :
Given:
[tex]f(x)=2x^3[/tex]To write:
The function when f(x) is stretched vertically by a factor of 5 and shifted 3 units left.
Explanation:
In general, a vertical stretch by a factor b and shift a units left is given by the equation
[tex]y=bf\left(x+a\right)[/tex]So, the new function becomes,
[tex]\begin{gathered} y=5f(x+3) \\ y=g(x)=5\times2(x+3)^3 \\ g(x)=10(x+3)^3 \end{gathered}[/tex]Final answer:
The new function is,
[tex]g(x)=10(x+3)^{3}[/tex]