Modeling with Rational Functions — Unit test

Question 600 • [INMT3] Integrated Math 3 Sem 1 (26-27)

Consider Which statement correctly uses limits to determine the end behavior of g(x)?

Answer

Limit of StartFraction 4 x + 9 Over x Superscript 6 Baseline + 1 EndFraction as x approaches plus-or-minus infinity = limit of StartFraction 4 Over 1 EndFraction as x approaches plus-or-minus infinity, so as x approaches infinity, g (x) approaches 4.

Limit of StartFraction 4 x + 9 Over x Superscript 6 Baseline + 1 EndFraction as x approaches plus-or-minus infinity = limit of StartFraction 4 Over x Superscript 5 EndFraction as x approaches plus-or-minus infinity, so as x approaches infinity, g (x) approaches 4.

Limit of StartFraction 4 x + 9 Over x Superscript 6 Baseline + 1 EndFraction as x approaches plus-or-minus infinity = limit of StartFraction 4 x Over 1 EndFraction as x approaches plus-or-minus infinity, so as x approaches infinity, g (x) approaches infinity.

Explanation

The denominator has degree 6, while the numerator has degree 1, so the fraction approaches 0 as x approaches either positive or negative infinity. Dividing the numerator and denominator by x⁶ gives (4/x⁵ + 9/x⁶)/(1 + 1/x⁶), whose limit is 0. Thus the end behavior is described by choice C: g(x) approaches 0.

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