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(6x-18)/(x^2-3*x)

  • How to use it?

  • Graphing y =:
  • x^2+3x-10
  • -x^2+4x-2
  • x^2-2x+2
  • ((x-1)/(x+1))^2

  • Identical expressions

  • (6x- eighteen)/(x^ two - three *x)
  • (6x minus 18) divide by (x squared minus 3 multiply by x)
  • (6x minus eighteen) divide by (x to the power of two minus three multiply by x)
  • (6x-18)/(x2-3*x)
  • 6x-18/x2-3*x
  • (6x-18)/(x²-3*x)
  • (6x-18)/(x to the power of 2-3*x)
  • (6x-18)/(x^2-3x)
  • (6x-18)/(x2-3x)
  • 6x-18/x2-3x
  • 6x-18/x^2-3x
  • (6x-18) divide by (x^2-3*x)

  • Similar expressions

  • (6x-18)/(x^2+3*x)
  • (6x+18)/(x^2-3*x)
Plotting a function graph/ (6x-18)/(x^2-3*x)

Graphing y = (6x-18)/(x^2-3*x)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
       6*x - 18
f(x) = --------
        2      
       x  - 3*x
f(x)=6x−18x2−3xf{\left(x \right)} = \frac{6 x - 18}{x^{2} - 3 x} 
f = (6*x - 1*18)/(x^2 - 3*x)
The graph of the function
02468-8-6-4-2-1010-250250
The domain of the function
The points at which the function is not precisely defined:
x1=0x_{1} = 0
x2=3x_{2} = 3
The points of intersection with the X-axis coordinate
Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
6x−18x2−3x=0\frac{6 x - 18}{x^{2} - 3 x} = 0
Solve this equation
Solution is not found,
it's possible that the graph doesn't intersect the axis X
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to (6*x - 1*18)/(x^2 - 3*x).
(−1)18+6⋅002−3⋅0\frac{\left(-1\right) 18 + 6 \cdot 0}{0^{2} - 3 \cdot 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
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
the first derivative
(−2x+3)(6x−18)(x2−3x)2+6x2−3x=0\frac{\left(- 2 x + 3\right) \left(6 x - 18\right)}{\left(x^{2} - 3 x\right)^{2}} + \frac{6}{x^{2} - 3 x} = 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
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
the second derivative
−12⋅(1+2x−3x−3−(2x−3)2x(x−3))x2(x−3)=0- \frac{12 \cdot \left(1 + \frac{2 x - 3}{x - 3} - \frac{\left(2 x - 3\right)^{2}}{x \left(x - 3\right)}\right)}{x^{2} \left(x - 3\right)} = 0
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Vertical asymptotes
Have:
x1=0x_{1} = 0
x2=3x_{2} = 3
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞(6x−18x2−3x)=0\lim_{x \to -\infty}\left(\frac{6 x - 18}{x^{2} - 3 x}\right) = 0
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=0y = 0
lim⁡x→∞(6x−18x2−3x)=0\lim_{x \to \infty}\left(\frac{6 x - 18}{x^{2} - 3 x}\right) = 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 (6*x - 1*18)/(x^2 - 3*x), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(6x−18x(x2−3x))=0\lim_{x \to -\infty}\left(\frac{6 x - 18}{x \left(x^{2} - 3 x\right)}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
lim⁡x→∞(6x−18x(x2−3x))=0\lim_{x \to \infty}\left(\frac{6 x - 18}{x \left(x^{2} - 3 x\right)}\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(-x) и f = -f(-x).
So, check:
6x−18x2−3x=−6x−18x2+3x\frac{6 x - 18}{x^{2} - 3 x} = \frac{- 6 x - 18}{x^{2} + 3 x}
- No
6x−18x2−3x=−−6x−18x2+3x\frac{6 x - 18}{x^{2} - 3 x} = - \frac{- 6 x - 18}{x^{2} + 3 x}
- No
so, the function
not is
neither even, nor odd
The graph
Graphing y = (6x-18)/(x^2-3*x)
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