Section 4.6 class notes_0

# Section 4.6 class notes_0 - Section 4.6 Rational Functions...

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Section 4.6 Rational Functions and Their Graphs Definition Rational Function A rational function is a function of the form ( ) ( ) ( ) = g x f x h x where g and h are polynomial functions such Objective 1 : Finding the Domain and Intercepts of Rational Functions Rational functions are defined for all values of x except those for which the denominator ( ) h x is equal to zero. If ( ) f x has a y- intercept, it can be found by evaluating (0) f provided that (0) f is defined. If ( ) f x has any x- intercepts, they can be found by solving the equation ( ) 0 = g x (provided that g and h do not share a common factor). 4.6.1-5 For the given rational function, determine the following: a) the domain b) the y -intercept (if any) c) the x -intercepts Objective 2 : Identifying Vertical Asymptotes Definition Vertical Asymptote The vertical line x a = is a vertical asymptote of a function ( ) y f x = if at least one of the following occurs: ( ) as f x x a + → ∞ ( ) as f x x a + → -∞ ( ) as f x x a - → ∞ ( ) as f x x a - → -∞ A rational function of the form ( ) ( ) ( ) = g x f x h x where ( ) g x and ( ) h x have no common factors will have a vertical asymptote at x a = if ( ) 0 = h a . ( ) y f x = ( ) y f x = ( ) y f x = ( ) y f x = x a = x a = x a = x a = that ( ) 0. h x

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( ) y f x = It is essential to cancel any common factors before locating the vertical asymptotes
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Section 4.6 class notes_0 - Section 4.6 Rational Functions...

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