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How to find symmetry of a rational function

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How to test a rational function for symmetry

To find the inverse of a rational function y = f(x): Replace f(x) with y. Interchange x and y. Solve the resultant equation for y. The result would give the inverse f-1 (x). Example: Find the inverse of the rational function f(x) = (2x - 1) / (x + 3).

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Master Graphing rational functions Part 2 using symmetry

f ( y) = 4 a 2 y + y. which has the following property: f ( − y) = − 4 a 2 y − y = − f ( y) which means that f ( y) is an odd function, point symmetric around the origin, hence f ( x) is

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Function symmetry introduction (video)

Definition. If f (−x)= f (x) f ( − x) = f ( x) for all x x in the domain of f f, then f f is an even function. An even function is symmetric about the y y -axis. If f (−x)= −f (x) f ( − x) = − f ( x) for all x x in

asymptotes.pdf

Determining asymptotes is actually a fairly simple process. First, let’s start with the rational function, f (x) = axn +⋯ bxm +⋯ f ( x) = a x n + ⋯ b x m + ⋯. where n n is the largest exponent in the numerator and m m is the largest

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