Question

Consider the rational function $f(x) = \frac{8x + 14}{2x - 12}$. a. What monomial expression best estimates the behavior of $8x + 14$ as $x \to \pm \infty$? b. What monomial expression best estimates the behavior of $2x - 12$ as $x \to \pm \infty$? c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the behavior of $\frac{8x + 14}{2x - 12}$ as $x \to \pm \infty$. Simplify your answer as much as possible.

          Consider the rational function $f(x) = \frac{8x + 14}{2x - 12}$.
a. What monomial expression best estimates the behavior of $8x + 14$ as $x \to \pm \infty$? 
b. What monomial expression best estimates the behavior of $2x - 12$ as $x \to \pm \infty$? 
c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the behavior of $\frac{8x + 14}{2x - 12}$ as $x \to \pm \infty$. Simplify your answer as much as possible.

Consider the rational function f(x) = (8x + 14)/(2x - 12).
a. What monomial expression best estimates the behavior of 8x + 14 as x →±∞?
b. What monomial expression best estimates the behavior of 2x - 12 as x →±∞?
c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the behavior of (8x + 14)/(2x - 12) as x →±∞. Simplify your answer as much as possible.

Added by Gregory S.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Teresa Fuston

12/06/2021

Step 1

As x approaches infinity, the term 8x dominates the behavior of the function, so the monomial expression that best estimates the behavior of 8x+14 as x approaches infinity is 8x. Show more…

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Consider the rational function f(x) = 8x+14 / 2-12x. a. What monomial expression best estimates the behavior of 8x+14 as x approaches infinity? b. What monomial expression best estimates the behavior of 2x -12 as x approaches infinity? c. Using your results from parts a and b, write a ratio of monomial expressions that best estimates the behavior of 8x+14 / 2-12x as x approaches infinity. Simplify your answer as much as possible.