Symmetry and Asymptotes. f(-x) = f(x)EvenSymmetrical wrt y-axis f(-x) = -f(x)OddSymmetrical wrt origin Even Neither Odd Even Odd.

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Presentation transcript:

Symmetry and Asymptotes

f(-x) = f(x)EvenSymmetrical wrt y-axis f(-x) = -f(x)OddSymmetrical wrt origin Even Neither Odd Even Odd

Asymptotes VERTICAL – values of x which make the denominator 0 HORIZONTAL – take the limit as x approaches infinity of f(x) OBLIQUE OR SLANT – will occur when degree of numerator is ONE MORE than degree of the denominator Slant asymptote is

a. Find the symmetry b. Find the intercepts c. Find the asymptotes No slant d. Find the ‘number line’ -2 y’ y’’ + __ _

No Symmetry Asymptotes x = -2 y = 1 -2 y’ y’’ + __ _ (0, 1.5) (-3, 0)

a. Find the symmetry b. Find the intercepts c. Find the asymptotes

d. Find the ‘number line’ + _ _ _ 0 y’ y’’ 24 + _ + +

Symmetry – None (0, 1) (-2, 0) (1, 0) Asymptotes y = x + 3 x = 2 + _ _ _ 0 y’ y’’ 24 + _ + +