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Vertical asymptote
- Intro Lesson6:31
- Lesson: 114:28
- Lesson: 1a10:06
- Lesson: 1b19:33
- Lesson: 1c21:17
- Lesson: 2a4:44
- Lesson: 2b4:29
- Lesson: 2c2:35
- Lesson: 2d3:01
- Lesson: 2e3:41
- Lesson: 2f6:11
- Lesson: 2g3:35
- Lesson: 2h3:12
- Lesson: 2i3:58
- Lesson: 2j5:04
Vertical asymptote
Lessons
For a rational function: f(x)=denominatornumerator
Provided that the numerator and denominator have no factors in common (if there are, we have "points of discontinuity" as discussed in the previous section), vertical asymptotes can be determined as follows:
∙equations of vertical asymptotes: x = zeros of the denominator
i.e.f(x)=x(x+5)(3x−7)numerator; vertical asymptotes: x=0,x=−5,x=57
- IntroductionIntroduction to Vertical Asymptotes • How to determine vertical asymptotes of a rational function? • Exercise:
For the rational function: f(x)=(x)(2x+9)(x+5)(3x−7)(6x+11)(2x+9)(x−8)(6x+11)
i) Locate the points of discontinuity.
ii) Find the vertical asymptotes.
- 1.Graphing Rational Functions
Sketch each rational function by determining:
i) vertical asymptote.
ii) horizontal asymptotes
a)f(x)=2x+105b)g(x)=−2x2+3x+25x2−13x+6c)h(x)=20x−100x3 - 2.Identifying Characteristics of Rational Functions
Without sketching the graph, determine the following features for each rational function:
i) point of discontinuity
ii) vertical asymptote
iii) horizontal asymptote
iv) slant asymptote
a)a(x)=x+9x−9b)b(x)=x2+9x2−9c)c(x)=x2−9x2+9d)d(x)=x2−9x+9e)e(x)=x2−9x+3f)f(x)=x+9x2+9g)g(x)=−x2−9−x−9h)h(x)=−x2+9−x2−9i)i(x)=x+3x2−9j)j(x)=x2−3xx3−9x2