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: https://brainly.com/question/1033817

#LearnWithBrainly

Answer 2

The new function, f'(x) after the vertical stretch and the translation is; f'(x) = 2(x+4)⁴ + 2(x+4) + 6)

Vertical stretch and translation

Form the task content;

• The given function is; f(x)=x⁴+2x+6

After the stretch by a factor of 2: The resulting function is;

• 2f(x) = 2(x⁴+2x+6)

Following the stretch, a further transformation of 4 units is done to the right.

It therefore follows that the ultimate function is;

• f'(x) = 2(x+4)⁴ + 2(x+4) + 6)

Read more on transformations;

https://brainly.com/question/4289712