Question

F(x)=x4+2x+6 ; vertical stretch by a factor of 2, followed by a translation 4 units right

Answer 1

$h(x)=2(x-4)^4+4(x-4)+12$

Explanation:

• Vertical stretch is a non-rigid transformation because it causes a distortion in the graph of the function.
• Translation is a rigid transformation because the basic shape of the graph is unchanged.

Let:

$f(x) \ a \ function \ and \ g(x) \ the \ transformation \ of \ f(x): \\ \\ g(x)=cf(x) \\ \\ If \ c>1 \ is \ a \ vertical \ stretch$

$f(x) \ a \ function \ and \ g(x) \ the \ transformation \ of \ f(x): \\ \\ g(x)=f(x-c) \\ \\ For \ c>0 \ shift \ the \ graph \ c \ units \ right$

So, the transformations:

Vertical stretch by a factor of 2:

$g(x)=2f(x) \\ \\ g(x)=2(x^4+2x+6) \\ \\ g(x)=2x^4+4x+12$

Translation 4 units right:

$h(x)=2(x-4)^4+4(x-4)+12$

Learn more:

Transformations in real life problems: brainly.com/question/1033817

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