Graphing y = y/2

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       y
f(y) = -
       2

f{\left(y \right)} = \frac{y}{2}

f = y/2

The graph of the function

The points of intersection with the X-axis coordinate

Graph of the function intersects the axis Y at f = 0
so we need to solve the equation:

\frac{y}{2} = 0

Solve this equation
The points of intersection with the axis Y:

Analytical solution

y_{1} = 0

Numerical solution

y_{1} = 0

The points of intersection with the Y axis coordinate

The graph crosses Y axis when y equals 0:
substitute y = 0 to y/2.

\frac{0}{2}

The result:

f{\left(0 \right)} = 0

The point:

(0, 0)

Extrema of the function

In order to find the extrema, we need to solve the equation

\frac{d}{d y} f{\left(y \right)} = 0

(the derivative equals zero),
and the roots of this equation are the extrema of this function:

\frac{d}{d y} f{\left(y \right)} =

\frac{1}{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

\frac{d^{2}}{d y^{2}} f{\left(y \right)} = 0

(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:

\frac{d^{2}}{d y^{2}} f{\left(y \right)} =

0 = 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 y->+oo and y->-oo

\lim_{y \to -\infty}\left(\frac{y}{2}\right) = -\infty

Let's take the limit
so,
horizontal asymptote on the left doesn’t exist

\lim_{y \to \infty}\left(\frac{y}{2}\right) = \infty

Let's take the limit
so,
horizontal asymptote on the right doesn’t exist

Inclined asymptotes

Inclined asymptote can be found by calculating the limit of y/2, divided by y at y->+oo and y ->-oo

\lim_{y \to -\infty} \frac{1}{2} = \frac{1}{2}

Let's take the limit
so,
inclined asymptote equation on the left:

y = \frac{y}{2}

\lim_{y \to \infty} \frac{1}{2} = \frac{1}{2}

Let's take the limit
so,
inclined asymptote equation on the right:

y = \frac{y}{2}

Even and odd functions

Let's check, whether the function even or odd by using relations f = f(-y) и f = -f(-y).
So, check:

\frac{y}{2} = - \frac{y}{2}

- No

\frac{y}{2} = \frac{y}{2}

- No
so, the function
not is
neither even, nor odd