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Given f of x is equal to the quantity 8x plus 1 end quantity divided by the quantity 2x minus 9 end quantity, what is the end behavior of the function? As x → -∞, f(x) → 9 ; as x → ∞, f(x) → 9. As x → -∞, f(x) → -9; as x → ∞, f(x) → -9. As x → -∞, f(x) → -4; as x → ∞, f(x) → -4. As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.

Respuesta :

Using limits, it is found that the end behavior of the function is given as follows:

As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.

How to find the end behavior of a function f(x)?

The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.

In this problem, the function is:

[tex]f(x) = \frac{8x - 1}{2x - 9}[/tex]

Considering that x goes to infinity, for the limits, we consider only the terms with the highest exponents in the numerator and denominator, hence:

  • [tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} \frac{8x}{2x} = \lim_{x \rightarrow -\infty} 4 = 4[/tex].
  • [tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{8x}{2x} = \lim_{x \rightarrow \infty} 4 = 4[/tex].

Hence the correct statement is:

As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.

More can be learned about limits and end behavior at https://brainly.com/question/27950332

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