Show all work to identify the asymptotes and zero of the function f(x)=5x (over) x^2-25

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Step-by-step explanation:

The function will have a zero where the numerator is zero:

  5x = 0

  x = 0 . . . . divide by 5

The zero of the function is x=0.

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The function will have vertical asymptotes where the denominator is zero:

  x^2 -25 = 0

  x^2 = 25 . . . . add 25

  x = ±5 . . . . . . take the square root

The function will have vertical asymptotes at x = -5 and x = 5.

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When x gets large, the magnitude of the function is approximately ...

  5x/x^2 = 5/x

As x approaches infinity, this value approaches zero.

The function will have a horizontal asymptote at y = 0.

Step-by-step explanation:

The Call of the Wild is a story of transformation in which the old Buck—the civilized, moral Buck—must adjust to the harsher realities of life in the frosty North, where survival is the only imperative. Kill or be killed is the only morality among the dogs of the Klondike, as Buck realizes from the moment he steps off the boat and watches the violent death of his friend Curly. The wilderness is a cruel, uncaring world, where only the strong prosper. It is, one might say, a perfect Darwinian world, and London’s depiction of it owes much to Charles Darwin, who proposed the theory of evolution to explain the development of life on Earth and envisioned a natural world defined by fierce competition for scarce resources. The term often used to describe Darwin’s theory, although he did not coin it, is “the survival of the fittest,” a phrase that describes Buck’s experience perfectly. In the old, warmer world, he might have sacrificed his life out of moral considerations; now, however, he abandons any such considerations in order to survive.

But London is not content to make the struggle for survival the central theme of his novel; instead, his protagonist struggles toward a higher end, namely mastery. We see this struggle particularly in Buck’s conflict with Spitz, in his determination to become the lead dog on Francois and Perrault’s team, and, at the end of the novel, in the way that he battles his way to the leadership of the wolf pack. Buck does not merely want to survive; he wants to dominate—as do his rivals, dogs like Spitz. In this quest for domination, which is celebrated by London’s narrative, we can observe the influence of Friedrich Nietzsche, a German philosopher of the late nineteenth century. Nietzsche’s worldview held that the world was composed of masters, those who possessed what he called “the will to power,” and slaves, those who did not possess this will. Nietzsche delighted in using animal metaphors, comparing masters to “birds of prey” and “blonde beasts” and comparing slaves to sheep and other herd animals. London’s Buck, with his indomitable strength and fierce desire for mastery, is a canine version of Nietzsche’s masterful men, his Napoleon Bonapartes and Julius Caesars. Buck is a savage creature, in a sense, and hardly a moral one, but London, like Nietzsche, expects us to applaud this ferocity. His novel suggests that there is no higher destiny for man or beast than to struggle, and win, in the battle for mastery.