Question

Write a function that transforms f(x) = 2x^3 in the following way:stretch vertically by a factor of 5 and shift 3 units left.

Answer 1

Given:

`f(x)=2x^3`

To write:

The function when f(x) is stretched vertically by a factor of 5 and shifted 3 units left.

Step-by-step explanation:

In general, a vertical stretch by a factor b and shift a units left is given by the equation

`y=bf\left(x+a\right)`

So, the new function becomes,

`\begin{gathered} y=5f(x+3) \\ y=g(x)=5*2(x+3)^3 \\ g(x)=10(x+3)^3 \end{gathered}`

Final answer:

The new function is,

`g(x)=10(x+3)^(3)`