1. For the given algebraic function $$ f(x)=\frac{x^{5 / 2}-x^{1 / 2}}{x^{5 / 3}-x^{2 / 3}} $$ a) Find the domain of the function. b) Check whether the function is even, odd or neither. c) Find all the vertical and horizontal asymptotes.

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Hilton Summers · Accepted Answer

a) The domain of the function is $$ [0, \infty) $$. b) The function is neither even nor odd. c) The function has a vertical asymptote at $$ x = 0 $$ and a horizontal asymptote at $$ y = \infty $$ as $$ x $$ approaches infinity. There is no horizontal asymptote as $$ x $$ approaches negative infinity.

1. For the given algebraic function \[ f(x)=\frac{x^{5 / 2}-x^{1 / 2}}{x^{5 / 3}-x^{2 / 3}} \] a) Find the domain of the function. b) Check whether the function is even, odd or neither. c) Find all the vertical and horizontal asymptotes.

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1. For the given algebraic function \[ f(x)=\frac{x^{5 / 2}-x^{1 / 2}}{x^{5 / 3}-x^{2 / 3}} \] a) Find the domain of the function. b) Check whether the function is even, odd or neither. c) Find all the vertical and horizontal asymptotes.

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