Find the End Behavior 2x^7+5x^4-6x^3+8x

Solution

endbehavior

as x \to + \infty, f (x) \to + \infty, and as x \to - \infty, f (x) \to - \infty

Solution steps

Domain of

2 x^{7} + 5 x^{4} - 6 x^{3} + 8 x : - \infty < x < \infty

x \to \infty lim (2 x^{7} + 5 x^{4} - 6 x^{3} + 8 x) = \infty

as x \to + \infty, f (x) \to + \infty

x \to - \infty lim (2 x^{7} + 5 x^{4} - 6 x^{3} + 8 x) = - \infty

as x \to - \infty, f (x) \to - \infty

as x \to + \infty, f (x) \to + \infty, and as x \to - \infty, f (x) \to - \infty