4.4 - 5.1 - Math 1310 Section 4.4 Section 4.4 Rational Function and their Graphs The objective in this section will be to identify the important

# 4.4 - 5.1 - Math 1310 Section 4.4 Section 4.4 Rational...

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Math 1310 Section 4.4 1 Section 4.4: Rational Function and their Graphs The objective in this section will be to identify the important features of a rational function and then to use them to sketch an accurate graph of the function. A rational function can be expressed as ݂ሺݔሻ ൌ ௣ሺ௫ሻ ௤ሺ௫ሻ where ݌ሺݔሻ and ݍሺݔሻ are polynomial functions and ݍሺݔሻ ് 0. Example 1: Find the domain of ݂ሺݔሻ ൌ ௫ିଶ ିଽ The features you will want to identify are: the locations of any holes in the graph of the function the locations of any vertical or horizontal asymptotes the locations of any x or y intercepts Vertical Asymptote of Rational Functions The line ݔ ൌ ܽ is a vertical asymptote of the graph of a function f if f ( x ) increases or decreases without bound as x approaches a . Basic example is ݂ሺݔሻ ൌ
Math 1310 Section 4.4 2 Locating Vertical Asymptotes and Holes Factor the numerator and denominator. Look at each factor in the denominator. If a factor cancels with a factor in the numerator, then there is a hole where that factor equals zero. If a factor does not cancel, then there is a vertical asymptote where that factor equals zero. ۳ܠ܉ܕܘܔ܍ ૛: Find any vertical asymptoteሺsሻ and/or holeሺsሻ of ݂ሺݔሻ ൌ ݔ െ 3ݔ െ 10 ݔ െ ݔ െ 6 Example 3: Find any vertical asymptote(s) and/or hole(s) of ݂ሺݔሻ ൌ ݔ ൅ 3ݔ െ 4 ݔ െ 9 Example 4: Find any vertical asymptote(s) and/or hole(s) of ݂ሺݔሻ ൌ ݔ െ 16 ݔ െ 2ݔ െ 8
Math 1310 Section 4.4 3 Horizontal Asymptote of Rational Functions The line