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mac1105_review_3 - REVIEW UNIT III L16 L24 FORMULAS TO...

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1 REVIEW UNIT III L16 – L24 FORMULAS TO MEMORIZE : Properties of Exponents ( 0, 1, 0, 1) a a b b > > : x y x y a a a + = x x y y a a a = ( ) y x x y a a = 1 x x a a = 0 1 a = ( ) x x x ab a b = x x x a a b b = Identities: log a x a x = ( 0 x > ), log x a a x = ( x is any real number) Properties of logarithms ( 0, 0, 0, 1, and 0 x y a a p > > > ): (a) log ( ) log log a a a xy x y = + (b) log log log a a a x x y y = (c) log log r a a x r x = (d) 1 log log p a a x x p = (e) log 1 a a = (f) log 1 0 a = Change-of-Base Theorem: ( ) log log , , 0 1 1 log b a b x x a b x a b a = > 1. Analyze the rational functions: (a) Find the vertical and horizontal or oblique asymptotes if 3 2 2 2 2 2( 5 )( 6) ( ) ( 10 25)( 3 2) x x x x f x x x x x = + + + . (b) Sketch the graph of the rational function: ( ) ( ) ( ) ( ) 2 2 2 4 3 ( ) 6 8 1 x x x f x x x x + = + + . (Find the domain, symmetry, holes, asymptotes, intercepts and points where the graph crosses its horizontal or oblique asymptote. If any of the above does not exist, write: None). 2. Find the equation of a rational function which has the following features: x-intercepts: 3 x = − (where it crosses the x-axis) and 0 x = (where it touches the x- axis) vertical asymptotes: 2 x = − (where it does not change the signs) and 1 x = (where it changes the signs)
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