2.8 Reciprocal and Rational Functions
and Equations of vertical and horizontal asymptotes
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Key Ideas
Key Ideas
The parameters in a function or equation correspond to geometrical features of a graph and can represent physical quantities in spatial dimensions.
Our spatial frame of reference affects the visible part of a function and by changing this “window” can show more or less of the function to best suit our needs.I understand that the graph of a reciprocal function is a Hyperbola
I can show that the reciprocal function is self-inverse
I can explain and demonstrate how to find the asymptotes of rational functions
Finding Vertical Asymptotes
Finding Vertical Asymptotes
https://www.youtube.com/watch?v=V137qmDN9Qw
MIT grad shows how to find the vertical asymptotes of a rational function and what they look like on a graph. To skip ahead: 1) For the STEPS TO FIND THE VERTICAL ASYMPTOTE(S) and an example with two vertical asymptotes, skip to 0:19. 2) For an example in which FACTORS CANCEL and that has one vertical asymptote and a HOLE, skip to 5:58. 3) For an example with NO VERTICAL ASYMPTOTES, skip to time 10:12.
Vertical Asymptotes
Vertical Asymptotes
Note that we will only have linear functions in the denominator.
https://www.youtube.com/watch?v=_qEOZNPce60
Finding Vertical Asymptotes of Rational Functions. In this video, I show what to look for, in order to find vertical asymptotes of rational functions, and do 4 examples of finding vertical asymptotes.
https://www.youtube.com/watch?v=DAwUVqq5vC0
Vertical Asymptotes of Rational Functions: Quick Way to Find Them, Another Example 1. Just another example of finding vertical asymptotes of rational functions.
How to find the Horizontal Asymptote
How to find the Horizontal Asymptote
The degree of a function is the highest power of x that appears in the polynomial. To find the horizontal asymptote, there are three easy cases.
1) If the degree of the numerator expression is less than the degree of the denominator expression, then the horizontal asymptote is y=0 (the x-axis).
2) If the degree of the numerator is equal to the degree of the denominator, then you can find the horizontal asymptote by dividing the first, highest term of the numerator by the first, highest term of the denominator. This will simplify to y = some constant (just a number).
3) If the degree of the numerator is greater than the degree of the denominator, then there is no horizontal asymptote.
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