Mister Exam

Other calculators

  • How to use it?

  • Graphing y =:
  • x/x^2+1 x/x^2+1
  • x/(x^2-1)
  • xe^(1/x)
  • xcosx

  • Identical expressions

  • (twenty *x^(one / four)- five / seven *x*sqrt(x)^(five)^ two - fourteen)^ seventeen
  • (20 multiply by x to the power of (1 divide by 4) minus 5 divide by 7 multiply by x multiply by square root of (x) to the power of (5) squared minus 14) to the power of 17
  • (twenty multiply by x to the power of (one divide by four) minus five divide by seven multiply by x multiply by square root of (x) to the power of (five) to the power of two minus fourteen) to the power of seventeen
  • (20*x^(1/4)-5/7*x*√(x)^(5)^2-14)^17
  • (20*x(1/4)-5/7*x*sqrt(x)(5)2-14)17
  • 20*x1/4-5/7*x*sqrtx52-1417
  • (20*x^(1/4)-5/7*x*sqrt(x)^(5)²-14)^17
  • (20*x to the power of (1/4)-5/7*x*sqrt(x) to the power of (5) to the power of 2-14) to the power of 17
  • (20x^(1/4)-5/7xsqrt(x)^(5)^2-14)^17
  • (20x(1/4)-5/7xsqrt(x)(5)2-14)17
  • 20x1/4-5/7xsqrtx52-1417
  • 20x^1/4-5/7xsqrtx^5^2-14^17
  • (20*x^(1 divide by 4)-5 divide by 7*x*sqrt(x)^(5)^2-14)^17

  • Similar expressions

  • (20*x^(1/4)-5/7*x*sqrt(x)^(5)^2+14)^17
  • (20*x^(1/4)+5/7*x*sqrt(x)^(5)^2-14)^17
Plotting a function graph/ (20*x^(1/4)-5/7*x*sqrt(x)^(5)^2-14)^17

Graphing y = (20*x^(1/4)-5/7*x*sqrt(x)^(5)^2-14)^17

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
                                    17
       /                    25     \  
       |   4 ___   5*x   ___       |  
f(x) = |20*\/ x  - ---*\/ x    - 14|  
       \            7              /
$$f{\left(x \right)} = \left(\left(20 \sqrt[4]{x} - \frac{5 x}{7} \left(\sqrt{x}\right)^{25}\right) - 14\right)^{17}$$ 
f = (20*x^(1/4) - 5*x/7*(sqrt(x))^25 - 14)^17
The graph of the function
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to (20*x^(1/4) - 5*x/7*(sqrt(x))^25 - 14)^17.
$$\left(-14 + \left(20 \sqrt[4]{0} - \frac{0 \cdot 5}{7} \left(\sqrt{0}\right)^{25}\right)\right)^{17}$$
The result:
$$f{\left(0 \right)} = -30491346729331195904$$
The point:
(0, -30491346729331195904)
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
$$\lim_{x \to -\infty} \left(\left(20 \sqrt[4]{x} - \frac{5 x}{7} \left(\sqrt{x}\right)^{25}\right) - 14\right)^{17} = \infty i$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty} \left(\left(20 \sqrt[4]{x} - \frac{5 x}{7} \left(\sqrt{x}\right)^{25}\right) - 14\right)^{17} = -\infty$$
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 (20*x^(1/4) - 5*x/7*(sqrt(x))^25 - 14)^17, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\left(\left(20 \sqrt[4]{x} - \frac{5 x}{7} \left(\sqrt{x}\right)^{25}\right) - 14\right)^{17}}{x}\right) = - \infty i$$
Let's take the limit
so,
inclined asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(\frac{\left(\left(20 \sqrt[4]{x} - \frac{5 x}{7} \left(\sqrt{x}\right)^{25}\right) - 14\right)^{17}}{x}\right) = -\infty$$
Let's take the limit
so,
inclined asymptote on the right doesn’t exist
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:
$$\left(\left(20 \sqrt[4]{x} - \frac{5 x}{7} \left(\sqrt{x}\right)^{25}\right) - 14\right)^{17} = \left(\frac{5 x \left(- x\right)^{\frac{25}{2}}}{7} + 20 \sqrt[4]{- x} - 14\right)^{17}$$
- No
$$\left(\left(20 \sqrt[4]{x} - \frac{5 x}{7} \left(\sqrt{x}\right)^{25}\right) - 14\right)^{17} = - \left(\frac{5 x \left(- x\right)^{\frac{25}{2}}}{7} + 20 \sqrt[4]{- x} - 14\right)^{17}$$
- No
so, the function
not is
neither even, nor odd
    © Mister Exam – Calculator