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Alfpfeu

Hello, when x tends to [tex]\infty[/tex] the term with the highest degree will lead the behaviour.

In other words.

[tex]\displaystyle \lim_{x\rightarrow+\infty} {x^4+3x^3-2x+7}\\\\=\lim_{x\rightarrow+\infty} {x^4}\\\\=+\infty\\\\\\\displaystyle \lim_{x\rightarrow-\infty} {x^4+3x^3-2x+7}\\\\=\lim_{x\rightarrow-\infty} {x^4}\\\\=+\infty[/tex]

So, the answer B is correct.

Thank you.

As x → - ∞, then y → ∞ and x → ∞, then y → ∞. Then the correct option is B.

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = x⁴ + 3x³ - 2x + 7

If the value of x approaches the negative infinity, then the value of the function will be

f(x) = x⁴ + 3x³ - 2x + 7

We know that the value of (x⁴ - 2x) is greater than the value of 3x³. Then the value of the function will approach the positive infinity.

If the value of x approaches the positive infinity, then the value of the function will be

f(x) = x⁴ + 3x³ - 2x + 7

We know that the value of (x⁴ + 3x³) is greater than the value of 2x. Then the value of the function will approach the positive infinity.

Thus, As x → - ∞, then y → ∞ and x → ∞, then y → ∞.

Then the correct option is B.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

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