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------------------------------------------------ Identify the function that reflects \( f(x) = 14x^3 − 7x^2 + 6 \) across the y-axis and shifts it 6 units up.

A. \( h(x) = 14x^3 + 7x^2 + 12 \)
B. \( h(x) = −14x^3 − 7x^2 + 12 \)
C. \( h(x) = −14x^3 − 7x^2 \)
D. \( h(x) = 14x^3 − 7x^2 \)

Answer :

The correct function after reflection across the y-axis and shifts it 6 units up is,

⇒ h (x) = - 14x³ - 7x² + 12

What is Function?

A relation between a set of inputs having one output each is called a function.

We have to given that;

The function is,

⇒ f (x) = 14x³ - 7x² + 6

Now, After reflection across the y-axis we get;

⇒ f (x) = f (- x)

⇒ f (-x) = 14 (-x)³ - 7 (-x)² + 6

⇒ f (-x) = - 14x³ - 7x² + 6

And, After shifts it 6 units up, we get;

⇒ f (x) = f (x) + 6

Hence, We get the value of function is,

⇒ h (x) = - 14x³ - 7x² + 6 + 6

⇒ h (x) = - 14x³ - 7x² + 12

Learn more about the function visit:

https://brainly.com/question/28793267

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Answer: there's no answer, the correct answer is f(x) = -14x3 + 7x2

Step-by-step explanation:

1. f(x) = 14x3 − 7x2 + 6

2. reflection over y-axis : f(x) = -14x3 + 7x2 - 6

3. shift 6 units up : f(x) = -14x3 + 7x2 - 6 + 6

4. f(x) = -14x3 + 7x2

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