N/A — Exam

Question 30 • Precalculus

Which statement correctly identifies an asymptote of g of x is equal to the fraction with numerator 42 x cubed minus 15 and denominator 7 x cubed minus 4 x squared minus 3 using limits?

Answer

limit x to plus or minus infinity of g times x is equal to 6 , so g of x has an asymptote at y is equal to 6 .

limit x to plus or minus infinity of g times x is equal to 6 , so g of x has an asymptote at x is equal to 6 .

limit x to plus or minus infinity of g times x is equal to 5 , so g of x has an asymptote at y is equal to 5 .

limit x to plus or minus infinity of g times x is equal to 5 , so g of x has an asymptote at x is equal to 5 .

Explanation

As x approaches either positive or negative infinity, the highest-degree terms determine the limit. The ratio of their coefficients is 42/7 = 6, so g(x) approaches 6. Therefore, the horizontal asymptote is y = 6; choice A states this correctly.

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