## Exponential Growth (a•xn)

### If a =1, n∈ℤ , -2 ≦ n ≦ 3

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If n=-2
y=1/x2
y>0 , x≠ 0 (Asymptote at x=0)

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If n=-1
y=1/x

x≠ 0 (Asymptote at x=0)

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If n=0
y=1/x2

Linear (y=mx+c)

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If n=1
y=x (Linear)

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If n=2

Turning point: (0,0)

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If n=3  Case 1
y=x3(Cubic)

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If n=3  Case 2
y=x3+x(Cubic)

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If n=3  Case 3
y=x(x-1)(x+3)(Cubic)
3 real and different roots
2 turning points

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## Limit Theory

y=1/x

As x ---->0
y ---->

x = 1 ,  y = 1
x = 1/2 , y = 2

x = 1/4 ,  y = 4
x = 1/10 , y = 10
x = 1/1000 , y = 1000