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  • How to use it?

  • Graphing y =:
  • x^5-x
  • -x^2+9
  • -x^2-6*x-5
  • x^2-6x+4

  • Identical expressions

  • five *sqrt(y)/ two
  • 5 multiply by square root of (y) divide by 2
  • five multiply by square root of (y) divide by two
  • 5*√(y)/2
  • 5sqrt(y)/2
  • 5sqrty/2
  • 5*sqrt(y) divide by 2
Plotting a function graph/ 5*sqrt(y)/2

Graphing y = 5*sqrt(y)/2

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The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
           ___
       5*\/ y 
f(y) = -------
          2
f(y)=5y2f{\left(y \right)} = \frac{5 \sqrt{y}}{2} 
f = (5*sqrt(y))/2
The graph of the function
0.01.02.03.04.05.06.07.08.09.010.0010
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:
5y2=0\frac{5 \sqrt{y}}{2} = 0
Solve this equation
The points of intersection with the axis Y:

Analytical solution
y1=0y_{1} = 0
Numerical solution
y1=0y_{1} = 0
The points of intersection with the Y axis coordinate
The graph crosses Y axis when y equals 0:
substitute y = 0 to (5*sqrt(y))/2.
502\frac{5 \sqrt{0}}{2}
The result:
f(0)=0f{\left(0 \right)} = 0
The point:
(0, 0)
Extrema of the function
In order to find the extrema, we need to solve the equation
ddyf(y)=0\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:
ddyf(y)=\frac{d}{d y} f{\left(y \right)} =
the first derivative
54y=0\frac{5}{4 \sqrt{y}} = 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
d2dy2f(y)=0\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:
d2dy2f(y)=\frac{d^{2}}{d y^{2}} f{\left(y \right)} =
the second derivative
−58y32=0- \frac{5}{8 y^{\frac{3}{2}}} = 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→−∞(5y2)=∞i\lim_{y \to -\infty}\left(\frac{5 \sqrt{y}}{2}\right) = \infty i
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡y→∞(5y2)=∞\lim_{y \to \infty}\left(\frac{5 \sqrt{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 (5*sqrt(y))/2, divided by y at y->+oo and y ->-oo
lim⁡y→−∞(52y)=0\lim_{y \to -\infty}\left(\frac{5}{2 \sqrt{y}}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
lim⁡y→∞(52y)=0\lim_{y \to \infty}\left(\frac{5}{2 \sqrt{y}}\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(-y) и f = -f(-y).
So, check:
5y2=5−y2\frac{5 \sqrt{y}}{2} = \frac{5 \sqrt{- y}}{2}
- No
5y2=−5−y2\frac{5 \sqrt{y}}{2} = - \frac{5 \sqrt{- y}}{2}
- No
so, the function
not is
neither even, nor odd
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