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-sqrt(-x^2)

  • How to use it?

  • Graphing y =:
  • |x|-x |x|-x
  • x^4-4x^2+5
  • x+cosx
  • -x^3-x-2

  • Identical expressions

  • -sqrt(-x^ two)
  • minus square root of ( minus x squared )
  • minus square root of ( minus x to the power of two)
  • -√(-x^2)
  • -sqrt(-x2)
  • -sqrt-x2
  • -sqrt(-x²)
  • -sqrt(-x to the power of 2)
  • -sqrt-x^2

  • Similar expressions

  • -sqrt(x^2)
  • sqrt(-x^2)
Plotting a function graph/ -sqrt(-x^2)

Graphing y = -sqrt(-x^2)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
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          /   2 
f(x) = -\/  -x
f(x)=−−x2f{\left(x \right)} = - \sqrt{- x^{2}} 
f = -sqrt(-x^2)
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:
−−x2=0- \sqrt{- x^{2}} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=0x_{1} = 0
Numerical solution
x1=0x_{1} = 0
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to -sqrt(-x^2).
−−02- \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
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
−i∣x∣x=0- \frac{i \left|{x}\right|}{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
−i(sign⁡(x)−∣x∣x)x=0- \frac{i \left(\operatorname{sign}{\left(x \right)} - \frac{\left|{x}\right|}{x}\right)}{x} = 0
Solve this equation
The roots of this equation
x1=−10x_{1} = -10
x2=−16x_{2} = -16
x3=−86x_{3} = -86
x4=14x_{4} = 14
x5=−88x_{5} = -88
x6=−92x_{6} = -92
x7=24x_{7} = 24
x8=−60x_{8} = -60
x9=−82x_{9} = -82
x10=−18x_{10} = -18
x11=22x_{11} = 22
x12=80x_{12} = 80
x13=−48x_{13} = -48
x14=60x_{14} = 60
x15=−56x_{15} = -56
x16=90x_{16} = 90
x17=−8x_{17} = -8
x18=26x_{18} = 26
x19=−4x_{19} = -4
x20=46x_{20} = 46
x21=−28x_{21} = -28
x22=−32x_{22} = -32
x23=40x_{23} = 40
x24=98x_{24} = 98
x25=−36x_{25} = -36
x26=−38x_{26} = -38
x27=−22x_{27} = -22
x28=−40x_{28} = -40
x29=−24x_{29} = -24
x30=66x_{30} = 66
x31=−52x_{31} = -52
x32=56x_{32} = 56
x33=88x_{33} = 88
x34=94x_{34} = 94
x35=−6x_{35} = -6
x36=−30x_{36} = -30
x37=76x_{37} = 76
x38=16x_{38} = 16
x39=−96x_{39} = -96
x40=−20x_{40} = -20
x41=44x_{41} = 44
x42=−62x_{42} = -62
x43=6x_{43} = 6
x44=−84x_{44} = -84
x45=12x_{45} = 12
x46=2x_{46} = 2
x47=38x_{47} = 38
x48=92x_{48} = 92
x49=−34x_{49} = -34
x50=72x_{50} = 72
x51=28x_{51} = 28
x52=68x_{52} = 68
x53=78x_{53} = 78
x54=20x_{54} = 20
x55=−50x_{55} = -50
x56=−94x_{56} = -94
x57=32x_{57} = 32
x58=64x_{58} = 64
x59=−100x_{59} = -100
x60=−54x_{60} = -54
x61=−66x_{61} = -66
x62=10x_{62} = 10
x63=58x_{63} = 58
x64=86x_{64} = 86
x65=34x_{65} = 34
x66=−68x_{66} = -68
x67=−12x_{67} = -12
x68=8x_{68} = 8
x69=62x_{69} = 62
x70=−64x_{70} = -64
x71=30x_{71} = 30
x72=−44x_{72} = -44
x73=−58x_{73} = -58
x74=−46x_{74} = -46
x75=50x_{75} = 50
x76=84x_{76} = 84
x77=74x_{77} = 74
x78=−14x_{78} = -14
x79=100x_{79} = 100
x80=−70x_{80} = -70
x81=−2x_{81} = -2
x82=−74x_{82} = -74
x83=−80x_{83} = -80
x84=−42x_{84} = -42
x85=42x_{85} = 42
x86=18x_{86} = 18
x87=4x_{87} = 4
x88=−26x_{88} = -26
x89=52x_{89} = 52
x90=−98x_{90} = -98
x91=48x_{91} = 48
x92=36x_{92} = 36
x93=−72x_{93} = -72
x94=−78x_{94} = -78
x95=82x_{95} = 82
x96=54x_{96} = 54
x97=−90x_{97} = -90
x98=70x_{98} = 70
x99=96x_{99} = 96
x100=−76x_{100} = -76

Сonvexity and concavity intervals:
Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Have no bends at the whole real axis
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞(−−x2)=−∞i\lim_{x \to -\infty}\left(- \sqrt{- x^{2}}\right) = - \infty i
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡x→∞(−−x2)=−∞i\lim_{x \to \infty}\left(- \sqrt{- x^{2}}\right) = - \infty i
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 -sqrt(-x^2), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(−i∣x∣x)=i\lim_{x \to -\infty}\left(- \frac{i \left|{x}\right|}{x}\right) = i
Let's take the limit
so,
inclined asymptote equation on the left:
y=ixy = i x
lim⁡x→∞(−i∣x∣x)=−i\lim_{x \to \infty}\left(- \frac{i \left|{x}\right|}{x}\right) = - i
Let's take the limit
so,
inclined asymptote equation on the right:
y=−ixy = - i x
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:
−−x2=−−x2- \sqrt{- x^{2}} = - \sqrt{- x^{2}}
- Yes
−−x2=−x2- \sqrt{- x^{2}} = \sqrt{- x^{2}}
- No
so, the function
is
even
The graph
Graphing y = -sqrt(-x^2)
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