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-
How to use it?
- Graphing y =:
- -6x^2+x+1
- x^2+2x-8
- (x+1)/(x-1)
- (x-1)/(x+1)
-
Identical expressions
- x^(6x-x^ two)
- x to the power of (6x minus x squared )
- x to the power of (6x minus x to the power of two)
- x(6x-x2)
- x6x-x2
- x^(6x-x²)
- x to the power of (6x-x to the power of 2)
- x^6x-x^2
-
Similar expressions
- x^(6x+x^2)
Graphing y = x^(6x-x^2)
The solution
You have entered
[src]
2
6*x - x
f(x) = x
$$f{\left(x \right)} = x^{- x^{2} + 6 x}$$
f = x^(-x^2 + 6*x)
The graph of the function
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:
$$x^{- x^{2} + 6 x} = 0$$
Solve this equation
The points of intersection with the axis X:
Numerical solution
$$x_{1} = -54$$
$$x_{2} = 24.3817230303778$$
$$x_{3} = 22.3991210478115$$
$$x_{4} = -42$$
$$x_{5} = -68$$
$$x_{6} = -94$$
$$x_{7} = -50$$
$$x_{8} = 64.25$$
$$x_{9} = 84.25$$
$$x_{10} = -30.0017403797255$$
$$x_{11} = 66.25$$
$$x_{12} = -92$$
$$x_{13} = 52.25$$
$$x_{14} = 72.25$$
$$x_{15} = 16.4889704951537$$
$$x_{16} = -36.0000000003398$$
$$x_{17} = -88$$
$$x_{18} = -66$$
$$x_{19} = -82$$
$$x_{20} = 9.00948551584209$$
$$x_{21} = 50.25$$
$$x_{22} = 82.25$$
$$x_{23} = -34.000000086796$$
$$x_{24} = 38.25$$
$$x_{25} = -72$$
$$x_{26} = -58$$
$$x_{27} = 18.4500190992735$$
$$x_{28} = 96.25$$
$$x_{29} = -98$$
$$x_{30} = 58.25$$
$$x_{31} = -52$$
$$x_{32} = 62.25$$
$$x_{33} = 30.2547571438968$$
$$x_{34} = 42.25$$
$$x_{35} = 60.25$$
$$x_{36} = 86.25$$
$$x_{37} = -74$$
$$x_{38} = -90$$
$$x_{39} = 34.25$$
$$x_{40} = -44$$
$$x_{41} = 76.25$$
$$x_{42} = 68.25$$
$$x_{43} = 100.25$$
$$x_{44} = 90.25$$
$$x_{45} = 44.25$$
$$x_{46} = -32.0000206558112$$
$$x_{47} = -80$$
$$x_{48} = -86$$
$$x_{49} = -64$$
$$x_{50} = 36.25$$
$$x_{51} = -84$$
$$x_{52} = 56.25$$
$$x_{53} = 28.3561813032928$$
$$x_{54} = 94.25$$
$$x_{55} = -96$$
$$x_{56} = 14.5440547157237$$
$$x_{57} = 12.6267809198562$$
$$x_{58} = 74.25$$
$$x_{59} = -78$$
$$x_{60} = 20.4212017849929$$
$$x_{61} = 92.25$$
$$x_{62} = 98.25$$
$$x_{63} = -48$$
$$x_{64} = -60$$
$$x_{65} = 40.25$$
$$x_{66} = -46$$
$$x_{67} = 78.25$$
$$x_{68} = 10.7617462961386$$
$$x_{69} = -100$$
$$x_{70} = -56$$
$$x_{71} = -38.0000000000022$$
$$x_{72} = -70$$
$$x_{73} = 32.2540232264424$$
$$x_{74} = 48.25$$
$$x_{75} = 46.25$$
$$x_{76} = 88.25$$
$$x_{77} = -40$$
$$x_{78} = 26.3676995979854$$
$$x_{79} = -62$$
$$x_{80} = -76$$
$$x_{81} = 80.25$$
$$x_{82} = 54.25$$
$$x_{83} = 70.25$$
so we need to solve the equation:
$$x^{- x^{2} + 6 x} = 0$$
Solve this equation
The points of intersection with the axis X:
Numerical solution
$$x_{1} = -54$$
$$x_{2} = 24.3817230303778$$
$$x_{3} = 22.3991210478115$$
$$x_{4} = -42$$
$$x_{5} = -68$$
$$x_{6} = -94$$
$$x_{7} = -50$$
$$x_{8} = 64.25$$
$$x_{9} = 84.25$$
$$x_{10} = -30.0017403797255$$
$$x_{11} = 66.25$$
$$x_{12} = -92$$
$$x_{13} = 52.25$$
$$x_{14} = 72.25$$
$$x_{15} = 16.4889704951537$$
$$x_{16} = -36.0000000003398$$
$$x_{17} = -88$$
$$x_{18} = -66$$
$$x_{19} = -82$$
$$x_{20} = 9.00948551584209$$
$$x_{21} = 50.25$$
$$x_{22} = 82.25$$
$$x_{23} = -34.000000086796$$
$$x_{24} = 38.25$$
$$x_{25} = -72$$
$$x_{26} = -58$$
$$x_{27} = 18.4500190992735$$
$$x_{28} = 96.25$$
$$x_{29} = -98$$
$$x_{30} = 58.25$$
$$x_{31} = -52$$
$$x_{32} = 62.25$$
$$x_{33} = 30.2547571438968$$
$$x_{34} = 42.25$$
$$x_{35} = 60.25$$
$$x_{36} = 86.25$$
$$x_{37} = -74$$
$$x_{38} = -90$$
$$x_{39} = 34.25$$
$$x_{40} = -44$$
$$x_{41} = 76.25$$
$$x_{42} = 68.25$$
$$x_{43} = 100.25$$
$$x_{44} = 90.25$$
$$x_{45} = 44.25$$
$$x_{46} = -32.0000206558112$$
$$x_{47} = -80$$
$$x_{48} = -86$$
$$x_{49} = -64$$
$$x_{50} = 36.25$$
$$x_{51} = -84$$
$$x_{52} = 56.25$$
$$x_{53} = 28.3561813032928$$
$$x_{54} = 94.25$$
$$x_{55} = -96$$
$$x_{56} = 14.5440547157237$$
$$x_{57} = 12.6267809198562$$
$$x_{58} = 74.25$$
$$x_{59} = -78$$
$$x_{60} = 20.4212017849929$$
$$x_{61} = 92.25$$
$$x_{62} = 98.25$$
$$x_{63} = -48$$
$$x_{64} = -60$$
$$x_{65} = 40.25$$
$$x_{66} = -46$$
$$x_{67} = 78.25$$
$$x_{68} = 10.7617462961386$$
$$x_{69} = -100$$
$$x_{70} = -56$$
$$x_{71} = -38.0000000000022$$
$$x_{72} = -70$$
$$x_{73} = 32.2540232264424$$
$$x_{74} = 48.25$$
$$x_{75} = 46.25$$
$$x_{76} = 88.25$$
$$x_{77} = -40$$
$$x_{78} = 26.3676995979854$$
$$x_{79} = -62$$
$$x_{80} = -76$$
$$x_{81} = 80.25$$
$$x_{82} = 54.25$$
$$x_{83} = 70.25$$
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty} x^{- x^{2} + 6 x} = \infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty} x^{- x^{2} + 6 x} = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = 0$$
$$\lim_{x \to -\infty} x^{- x^{2} + 6 x} = \infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty} x^{- x^{2} + 6 x} = 0$$
Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = 0$$
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of x^(6*x - x^2), divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{x^{- x^{2} + 6 x}}{x}\right) = \infty$$
Let's take the limit
so,
inclined asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(\frac{x^{- x^{2} + 6 x}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
$$\lim_{x \to -\infty}\left(\frac{x^{- x^{2} + 6 x}}{x}\right) = \infty$$
Let's take the limit
so,
inclined asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(\frac{x^{- x^{2} + 6 x}}{x}\right) = 0$$
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:
$$x^{- x^{2} + 6 x} = \left(- x\right)^{- x^{2} - 6 x}$$
- No
$$x^{- x^{2} + 6 x} = - \left(- x\right)^{- x^{2} - 6 x}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$x^{- x^{2} + 6 x} = \left(- x\right)^{- x^{2} - 6 x}$$
- No
$$x^{- x^{2} + 6 x} = - \left(- x\right)^{- x^{2} - 6 x}$$
- No
so, the function
not is
neither even, nor odd
The graph