DAY 27 PI 7 Intro Rational Functions SMART NOTES
Ready, Set, Go !
DAY 27
December 9/10, 2016
CLASS OPENER (Do NOW): December 09, 2016
PI 7 Inverse functions quiz PI 3 V4
Nov 30­11:58 AM
Oct 20­9:01 AM
Rational value:
Rational expression:
Rational function:
Nov 6­2:42 PM
Vertical Asymptote x = 0 (y­axis)
Oct 20­9:04 AM
DEFINITION OF VERTICAL AND HORIZONTAL
ASYMPTOTES
>>> The line x=a is a vertical asymptote of the graph if f(x) ±∞ as x a
Horizontal Asymptote y = 0 (x­axis)
Therefore:
R: all real values except 0
R: f(x)≠0
R: (-∞; 0)∪(0,∞)
>>> The line y=b is a horizontal asymptote of the graph if f(x) b as x ±∞ lim f(x) = x 0
Oct 20­9:05 AM
Nov 5­12:49 PM
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DAY 27 PI 7 Intro Rational Functions SMART NOTES
December 09, 2016
Find asymptotes and graph rational function below by hand:
a) g(x) = 3 x­2
y­int.:
x­int.:
Vertical asymptote:
Horizontal asymptote:
x ­4 1 2 3 5 g(x) Dec 9­10:17 AM
Nov 5­12:58 PM
Remember that you can use your knowledge about function transformations!!!
Horizontal shift, vertical shift
Jun 30­9:56 AM
Oct 20­9:06 AM
Find asymptotes and graph rational function below by hand:
b) h(x) = 2x ­ 1 x
y­int.:
x­int:
Vertical asymptote:
Horizontal asymptote:
x ­4 ­1 0 1/4 4 h(x)
Nov 5­12:58 PM
Oct 20­9:07 AM
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DAY 27 PI 7 Intro Rational Functions SMART NOTES
December 09, 2016
Nov 6­3:47 PM
Jun 30­9:49 AM
Jun 30­9:50 AM
Jun 30­9:51 AM
6. h(x) _ 1 (x­2)2 7. g(x) = 5(x+4)
x2+x­12
5(x+4) = 5(x+4)
x2+x­12 (x+4)(x­3)
Jun 30­9:54 AM
Jun 30­9:57 AM
3
DAY 27 PI 7 Intro Rational Functions SMART NOTES
December 09, 2016
Dec 9­3:03 PM
4