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Plotting a function graph/ e^(-n)

Graphing y = e^(-n)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
        -n
f(n) = E
f(n)=e−nf{\left(n \right)} = e^{- n} 
f = E^(-n)
The graph of the function
02468-8-6-4-2-1010040000
The points of intersection with the X-axis coordinate
Graph of the function intersects the axis N at f = 0
so we need to solve the equation:
e−n=0e^{- n} = 0
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis N
The points of intersection with the Y axis coordinate
The graph crosses Y axis when n equals 0:
substitute n = 0 to E^(-n).
e−0e^{- 0}
The result:
f(0)=1f{\left(0 \right)} = 1
The point:
(0, 1)
Extrema of the function
In order to find the extrema, we need to solve the equation
ddnf(n)=0\frac{d}{d n} f{\left(n \right)} = 0
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
ddnf(n)=\frac{d}{d n} f{\left(n \right)} =
the first derivative
−e−n=0- e^{- n} = 0
Solve this equation
Solutions are not found,
function may have no extrema
Inflection points
Let's find the inflection points, we'll need to solve the equation for this
d2dn2f(n)=0\frac{d^{2}}{d n^{2}} f{\left(n \right)} = 0
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
d2dn2f(n)=\frac{d^{2}}{d n^{2}} f{\left(n \right)} =
the second derivative
e−n=0e^{- n} = 0
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at n->+oo and n->-oo
lim⁡n→−∞e−n=∞\lim_{n \to -\infty} e^{- n} = \infty
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡n→∞e−n=0\lim_{n \to \infty} e^{- n} = 0
Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=0y = 0
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of E^(-n), divided by n at n->+oo and n ->-oo
lim⁡n→−∞(e−nn)=−∞\lim_{n \to -\infty}\left(\frac{e^{- n}}{n}\right) = -\infty
Let's take the limit
so,
inclined asymptote on the left doesn’t exist
lim⁡n→∞(e−nn)=0\lim_{n \to \infty}\left(\frac{e^{- n}}{n}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-n) и f = -f(-n).
So, check:
e−n=ene^{- n} = e^{n}
- No
e−n=−ene^{- n} = - e^{n}
- No
so, the function
not is
neither even, nor odd
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