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  • Graphing y =:
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  • x+|x|
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  • Identical expressions

  • fourteen *asin(eight ^x)
  • 14 multiply by arc sinus of e of (8 to the power of x)
  • fourteen multiply by arc sinus of e of (eight to the power of x)
  • 14*asin(8x)
  • 14*asin8x
  • 14asin(8^x)
  • 14asin(8x)
  • 14asin8x
  • 14asin8^x

  • Similar expressions

  • 14*arcsin(8^x)
Plotting a function graph/ 14*asin(8^x)

Graphing y = 14*asin(8^x)

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The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
              / x\
f(x) = 14*asin\8 /
f(x)=14asin⁡(8x)f{\left(x \right)} = 14 \operatorname{asin}{\left(8^{x} \right)} 
f = 14*asin(8^x)
The graph of the function
02468-8-6-4-2-1010020
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:
14asin⁡(8x)=014 \operatorname{asin}{\left(8^{x} \right)} = 0
Solve this equation
The points of intersection with the axis X:

Numerical solution
x1=−15.9649870906711x_{1} = -15.9649870906711
x2=−67.964987090676x_{2} = -67.964987090676
x3=−61.964987090676x_{3} = -61.964987090676
x4=−85.964987090676x_{4} = -85.964987090676
x5=−19.964987090676x_{5} = -19.964987090676
x6=−59.964987090676x_{6} = -59.964987090676
x7=−41.964987090676x_{7} = -41.964987090676
x8=−95.964987090676x_{8} = -95.964987090676
x9=−57.964987090676x_{9} = -57.964987090676
x10=−45.964987090676x_{10} = -45.964987090676
x11=−75.964987090676x_{11} = -75.964987090676
x12=−81.964987090676x_{12} = -81.964987090676
x13=−53.964987090676x_{13} = -53.964987090676
x14=−91.964987090676x_{14} = -91.964987090676
x15=−23.964987090676x_{15} = -23.964987090676
x16=−49.964987090676x_{16} = -49.964987090676
x17=−105.964987090676x_{17} = -105.964987090676
x18=−97.964987090676x_{18} = -97.964987090676
x19=−87.964987090676x_{19} = -87.964987090676
x20=−107.964987090676x_{20} = -107.964987090676
x21=−51.964987090676x_{21} = -51.964987090676
x22=−43.964987090676x_{22} = -43.964987090676
x23=−69.964987090676x_{23} = -69.964987090676
x24=−21.964987090676x_{24} = -21.964987090676
x25=−73.964987090676x_{25} = -73.964987090676
x26=−77.964987090676x_{26} = -77.964987090676
x27=−79.964987090676x_{27} = -79.964987090676
x28=−37.964987090676x_{28} = -37.964987090676
x29=−99.964987090676x_{29} = -99.964987090676
x30=−27.964987090676x_{30} = -27.964987090676
x31=−35.964987090676x_{31} = -35.964987090676
x32=−39.964987090676x_{32} = -39.964987090676
x33=−55.964987090676x_{33} = -55.964987090676
x34=−65.964987090676x_{34} = -65.964987090676
x35=−71.964987090676x_{35} = -71.964987090676
x36=−109.964987090676x_{36} = -109.964987090676
x37=−25.964987090676x_{37} = -25.964987090676
x38=−83.964987090676x_{38} = -83.964987090676
x39=−31.964987090676x_{39} = -31.964987090676
x40=−93.964987090676x_{40} = -93.964987090676
x41=−17.964987090676x_{41} = -17.964987090676
x42=−101.964987090676x_{42} = -101.964987090676
x43=−103.964987090676x_{43} = -103.964987090676
x44=−47.964987090676x_{44} = -47.964987090676
x45=−63.964987090676x_{45} = -63.964987090676
x46=−33.964987090676x_{46} = -33.964987090676
x47=−89.964987090676x_{47} = -89.964987090676
x48=−29.964987090676x_{48} = -29.964987090676
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to 14*asin(8^x).
14asin⁡(80)14 \operatorname{asin}{\left(8^{0} \right)}
The result:
f(0)=7πf{\left(0 \right)} = 7 \pi
The point:
(0, 7*pi)
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
14⋅8xlog⁡(8)1−82x=0\frac{14 \cdot 8^{x} \log{\left(8 \right)}}{\sqrt{1 - 8^{2 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
−14⋅8x(82x82x−1−1)log⁡(8)21−82x=0- \frac{14 \cdot 8^{x} \left(\frac{8^{2 x}}{8^{2 x} - 1} - 1\right) \log{\left(8 \right)}^{2}}{\sqrt{1 - 8^{2 x}}} = 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→−∞(14asin⁡(8x))=0\lim_{x \to -\infty}\left(14 \operatorname{asin}{\left(8^{x} \right)}\right) = 0
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=0y = 0
lim⁡x→∞(14asin⁡(8x))=−∞i\lim_{x \to \infty}\left(14 \operatorname{asin}{\left(8^{x} \right)}\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 14*asin(8^x), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(14asin⁡(8x)x)=0\lim_{x \to -\infty}\left(\frac{14 \operatorname{asin}{\left(8^{x} \right)}}{x}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
True

Let's take the limit
so,
inclined asymptote equation on the right:
y=xlim⁡x→∞(14asin⁡(8x)x)y = x \lim_{x \to \infty}\left(\frac{14 \operatorname{asin}{\left(8^{x} \right)}}{x}\right)
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:
14asin⁡(8x)=14asin⁡(8−x)14 \operatorname{asin}{\left(8^{x} \right)} = 14 \operatorname{asin}{\left(8^{- x} \right)}
- No
14asin⁡(8x)=−14asin⁡(8−x)14 \operatorname{asin}{\left(8^{x} \right)} = - 14 \operatorname{asin}{\left(8^{- x} \right)}
- No
so, the function
not is
neither even, nor odd
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