Asymptotes Next slide © Annie Patton.

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Presentation transcript:

Asymptotes Next slide © Annie Patton

Aim of Lesson To introduce what an asymptote is, the difference in a horizontal and vertical asymptote and how to find these. Next slide © Annie Patton

What is an asymptote? -6 -4 -2 2 4 6 x y Vertical An asymptote is a line, to which a curve gets closer and closer without touching. Horizontal Next slide © Annie Patton

How to find a Vertical Asymptote Note it will be a line. y 10 x -4 -3 -2 -1 1 2 3 4 5 6 -10 Next slide © Annie Patton

How to find a Horizontal Asymptote Note it will be a line. 10 x -4 -3 -2 -1 1 2 3 4 5 6 -10 Next slide © Annie Patton

Do all curves have asymptotes? No Next slide © Annie Patton

Next slide © Annie Patton

-10 10 -5 y 15 10 5 x Next slide © Annie Patton

10 y 5 x -5 5 10 Next slide © Annie Patton

Leaving Certificate 2005 Higher Level Paper 1 no 6(c)(ii) Start clicking when you want to see the answer. 6 y 5 4 3 2 1 x -6 -4 -2 2 4 6 8 -1 To verify which quadrants the asymptotes are in, substitute in a point, for example x=4. -2 -3 -4 Next slide © Annie Patton

Next slide Leaving Certificate 2005 Higher Level Paper 1 no 6(c)(iii) Start clicking when you want to see the answer. 4 y 3 (x, y) (x, y) 2 1 (1,1) (1,1) (2-x,2-y) x -5 5 -1 -2 -3 -4 © Annie Patton Next slide

Homework © Annie Patton Next slide

Revision. What is an asymptote? -6 -4 -2 2 4 6 x y Vertical An asymptote is a line, to which a curve gets closer and closer without touching. Horizontal Next slide © Annie Patton

Revision. How to find a Vertical Asymptote Note it will be a line. y 10 x -4 -3 -2 -1 1 2 3 4 5 6 -10 Next slide © Annie Patton

Revision. How to find a Horizontal Asymptote Note it will be a line. 10 x -4 -3 -2 -1 1 2 3 4 5 6 -10 © Annie Patton