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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.

Sagot :

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]

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