1. Asymptotes
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2. Aim of Lesson
To introduce what an asymptote is, the difference in a horizontal and vertical asymptote and how to find these.
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3. 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
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4. 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
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5. 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
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6. Do all curves have asymptotes?No
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7. Next slide
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8. -10 10 -5 y 15 10 5 x
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9. 10 y 5 x -5 5 10
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10. 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
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11. 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
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12. Homework
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13. 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
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14. 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
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15. 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
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