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  • How to use it?

  • Graphing y =:
  • x^3-12x+1
  • (x^2-x-2)/(x-2)
  • -x/2
  • (x^2-6x+13)/(x-3)

  • Identical expressions

  • ln* one /(x^ two -4x+ eight)
  • ln multiply by 1 divide by (x squared minus 4x plus 8)
  • ln multiply by one divide by (x to the power of two minus 4x plus eight)
  • ln*1/(x2-4x+8)
  • ln*1/x2-4x+8
  • ln*1/(x²-4x+8)
  • ln*1/(x to the power of 2-4x+8)
  • ln1/(x^2-4x+8)
  • ln1/(x2-4x+8)
  • ln1/x2-4x+8
  • ln1/x^2-4x+8
  • ln*1 divide by (x^2-4x+8)

  • Similar expressions

  • ln*1/(x^2-4x-8)
  • ln*1/(x^2+4x+8)
Plotting a function graph/ ln*1/(x^2-4x+8)

Graphing y = ln*1/(x^2-4x+8)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
          log(1)   
f(x) = ------------
        2          
       x  - 4*x + 8
f(x)=log⁡(1)(x2−4x)+8f{\left(x \right)} = \frac{\log{\left(1 \right)}}{\left(x^{2} - 4 x\right) + 8} 
f = log(1)/(x^2 - 4*x + 8)
The graph of the function
02468-8-6-4-2-101001
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:
log⁡(1)(x2−4x)+8=0\frac{\log{\left(1 \right)}}{\left(x^{2} - 4 x\right) + 8} = 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 log(1)/(x^2 - 4*x + 8).
log⁡(1)(02−0)+8\frac{\log{\left(1 \right)}}{\left(0^{2} - 0\right) + 8}
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
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
(4−2x)log⁡(1)((x2−4x)+8)2=0\frac{\left(4 - 2 x\right) \log{\left(1 \right)}}{\left(\left(x^{2} - 4 x\right) + 8\right)^{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
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
2(4(x−2)2x2−4x+8−1)log⁡(1)(x2−4x+8)2=0\frac{2 \left(\frac{4 \left(x - 2\right)^{2}}{x^{2} - 4 x + 8} - 1\right) \log{\left(1 \right)}}{\left(x^{2} - 4 x + 8\right)^{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 x->+oo and x->-oo
lim⁡x→−∞(log⁡(1)(x2−4x)+8)=0\lim_{x \to -\infty}\left(\frac{\log{\left(1 \right)}}{\left(x^{2} - 4 x\right) + 8}\right) = 0
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=0y = 0
lim⁡x→∞(log⁡(1)(x2−4x)+8)=0\lim_{x \to \infty}\left(\frac{\log{\left(1 \right)}}{\left(x^{2} - 4 x\right) + 8}\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 log(1)/(x^2 - 4*x + 8), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(log⁡(1)x((x2−4x)+8))=0\lim_{x \to -\infty}\left(\frac{\log{\left(1 \right)}}{x \left(\left(x^{2} - 4 x\right) + 8\right)}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
lim⁡x→∞(log⁡(1)x((x2−4x)+8))=0\lim_{x \to \infty}\left(\frac{\log{\left(1 \right)}}{x \left(\left(x^{2} - 4 x\right) + 8\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:
log⁡(1)(x2−4x)+8=log⁡(1)x2+4x+8\frac{\log{\left(1 \right)}}{\left(x^{2} - 4 x\right) + 8} = \frac{\log{\left(1 \right)}}{x^{2} + 4 x + 8}
- No
log⁡(1)(x2−4x)+8=−log⁡(1)x2+4x+8\frac{\log{\left(1 \right)}}{\left(x^{2} - 4 x\right) + 8} = - \frac{\log{\left(1 \right)}}{x^{2} + 4 x + 8}
- No
so, the function
not is
neither even, nor odd
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