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  • Graphing y =:
  • x^2+3x-10
  • x^2+3x-18
  • -x^2+3x+4
  • x²-2x+8

  • Identical expressions

  • three ^tgx×arcsin(7x^ four)
  • 3 to the power of tgx×arc sinus of (7x to the power of 4)
  • three to the power of tgx×arc sinus of (7x to the power of four)
  • 3tgx×arcsin(7x4)
  • 3tgx×arcsin7x4
  • 3^tgx×arcsin(7x⁴)
  • 3^tgx×arcsin7x^4
Plotting a function graph/ 3^tgx×arcsin(7x^4)

Graphing y = 3^tgx×arcsin(7x^4)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
        tan(x)     /   4\
f(x) = 3      *asin\7*x /
f(x)=3tan⁡(x)asin⁡(7x4)f{\left(x \right)} = 3^{\tan{\left(x \right)}} \operatorname{asin}{\left(7 x^{4} \right)} 
f = 3^tan(x)*asin(7*x^4)
The graph of the function
02468-8-6-4-2-101002
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:
3tan⁡(x)asin⁡(7x4)=03^{\tan{\left(x \right)}} \operatorname{asin}{\left(7 x^{4} \right)} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=0x_{1} = 0
Numerical solution
x1=−80.074868892622x_{1} = -80.074868892622
x2=−51.8040154624648x_{2} = -51.8040154624648
x3=0x_{3} = 0
x4=−29.8117702392131x_{4} = -29.8117702392131
x5=−95.7890397178945x_{5} = -95.7890397178945
x6=36.1642345681226x_{6} = 36.1642345681226
x7=−7.81966445428965x_{7} = -7.81966445428965
x8=−73.7964262390778x_{8} = -73.7964262390778
x9=14.1723366037438x_{9} = 14.1723366037438
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to 3^tan(x)*asin(7*x^4).
3tan⁡(0)asin⁡(7⋅04)3^{\tan{\left(0 \right)}} \operatorname{asin}{\left(7 \cdot 0^{4} \right)}
The result:
f(0)=0f{\left(0 \right)} = 0
The point:
(0, 0)
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
True

Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=lim⁡x→−∞(3tan⁡(x)asin⁡(7x4))y = \lim_{x \to -\infty}\left(3^{\tan{\left(x \right)}} \operatorname{asin}{\left(7 x^{4} \right)}\right)
True

Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=lim⁡x→∞(3tan⁡(x)asin⁡(7x4))y = \lim_{x \to \infty}\left(3^{\tan{\left(x \right)}} \operatorname{asin}{\left(7 x^{4} \right)}\right)
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of 3^tan(x)*asin(7*x^4), divided by x at x->+oo and x ->-oo
True

Let's take the limit
so,
inclined asymptote equation on the left:
y=xlim⁡x→−∞(3tan⁡(x)asin⁡(7x4)x)y = x \lim_{x \to -\infty}\left(\frac{3^{\tan{\left(x \right)}} \operatorname{asin}{\left(7 x^{4} \right)}}{x}\right)
True

Let's take the limit
so,
inclined asymptote equation on the right:
y=xlim⁡x→∞(3tan⁡(x)asin⁡(7x4)x)y = x \lim_{x \to \infty}\left(\frac{3^{\tan{\left(x \right)}} \operatorname{asin}{\left(7 x^{4} \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:
3tan⁡(x)asin⁡(7x4)=3−tan⁡(x)asin⁡(7x4)3^{\tan{\left(x \right)}} \operatorname{asin}{\left(7 x^{4} \right)} = 3^{- \tan{\left(x \right)}} \operatorname{asin}{\left(7 x^{4} \right)}
- No
3tan⁡(x)asin⁡(7x4)=−3−tan⁡(x)asin⁡(7x4)3^{\tan{\left(x \right)}} \operatorname{asin}{\left(7 x^{4} \right)} = - 3^{- \tan{\left(x \right)}} \operatorname{asin}{\left(7 x^{4} \right)}
- No
so, the function
not is
neither even, nor odd
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