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Plotting a function graph/ 1/n

Graphing y = 1/n

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
       1
f(n) = -
       n
f(n)=1nf{\left(n \right)} = \frac{1}{n} 
f = 1/n
The graph of the function
02468-8-6-4-2-1010-5050
The domain of the function
The points at which the function is not precisely defined:
n1=0n_{1} = 0
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:
1n=0\frac{1}{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 1/n.
10\frac{1}{0}
The result:
f(0)=∞~f{\left(0 \right)} = \tilde{\infty}
sof doesn't intersect Y
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
−1n2=0- \frac{1}{n^{2}} = 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
2n3=0\frac{2}{n^{3}} = 0
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Vertical asymptotes
Have:
n1=0n_{1} = 0
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at n->+oo and n->-oo
lim⁡n→−∞1n=0\lim_{n \to -\infty} \frac{1}{n} = 0
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=0y = 0
lim⁡n→∞1n=0\lim_{n \to \infty} \frac{1}{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 1/n, divided by n at n->+oo and n ->-oo
lim⁡n→−∞1n2=0\lim_{n \to -\infty} \frac{1}{n^{2}} = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
lim⁡n→∞1n2=0\lim_{n \to \infty} \frac{1}{n^{2}} = 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:
1n=−1n\frac{1}{n} = - \frac{1}{n}
- No
1n=1n\frac{1}{n} = \frac{1}{n}
- Yes
so, the function
is
odd
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