What is the end behavior of the function $f (x) = x^{3} + 2 x^{2} + 4 x + 5$ $f(x) = x^3 + 2x^2 + 4x + 5$ ?

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What is the end behavior of the function $f (x) = x^{3} + 2 x^{2} + 4 x + 5$ $f(x) = x^3 + 2x^2 + 4x + 5$ ?

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Answer 1 · 2015-08-21T18:43:21

The end behaviour of a polynomial function is determined by the term of highest degree, in this case $x^{3}$ $x^3$ .

Hence $f (x) \to + \infty$ $f(x)->+oo$ as $x \to + \infty$ $x->+oo$ and $f (x) \to - \infty$ $f(x)->-oo$ as $x \to - \infty$ $x->-oo$ .

Explanation:

For large values of $x$ $x$ , the term of highest degree will be much larger than the other terms, which can effectively be ignored. Since the coefficient of $x^{3}$ $x^3$ is positive and its degree is odd, the end behaviour is $f (x) \to + \infty$ $f(x)->+oo$ as $x \to + \infty$ $x->+oo$ and $f (x) \to - \infty$ $f(x)->-oo$ as $x \to - \infty$ $x->-oo$ .

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What is the end behavior of the function $f (x) = x^{3} + 2 x^{2} + 4 x + 5$ $f(x) = x^3 + 2x^2 + 4x + 5$ ?

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What is the end behavior of the function $f (x) = x^{3} + 2 x^{2} + 4 x + 5$ $f(x) = x^3 + 2x^2 + 4x + 5$ ?