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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
1 REVIEW UNIT III L16 – L24 FORMULAS TO MEMORIZE : Properties of Exponents (0 , 1 , 0 ,1 ) aa b b >≠ > : x yx y aa a + ⋅= x x y y a a a = ( ) y x xy = 1 x x a a = 0 1 a = ( ) x x x ab a b =⋅ x x x bb ⎛⎞ = ⎜⎟ ⎝⎠ Identities: log a x ax = ( 0 x > ), log x a = ( x is any real number) Properties of logarithms ( 0, 0, 0, 1, and 0 xyaa p >>>≠ ): (a) log ( ) log log a x y =+ (b) log log log a x x y y =− (c) log log r x rx = (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 xa b x a b a = 1. Analyze the rational functions: (a) Find the vertical and horizontal or oblique asymptotes if 32 2 22 2( 5 )( 6) (1 0 2 5 ) (3 2 ) xx x x fx x x −− = −+ + + . (b) Sketch the graph of the rational function: ( )( ) 2 2 24 3 68 1 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) asymptote: oblique hole: (4 , 0 )
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online