Consider f of x is equal to the fraction with numerator 7 x squared plus x plus 1 and denominator x to the 4th power plus 1 Which statement correctly uses limits to determine the end behavior of f of x ?

The denominator has degree 4, while the numerator has degree 2, so the fraction approaches 0 as x grows in either direction. Dividing the numerator and denominator by x⁴ gives (7/x² + 1/x³ + 1/x⁴)/(1 + 1/x⁴), whose limit is 0. Choice B expresses this end behavior; the function does not approach 7 or infinity.

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