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(11-17x^2)/x
Plotting a function graph/ (11-17x^2)/x

Graphing y = (11-17x^2)/x

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The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

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       11 - 17*x 
f(x) = ----------
           x
f(x)=−17x2+11xf{\left(x \right)} = \frac{- 17 x^{2} + 11}{x} 
f = (11 - 17*x^2)/x
The graph of the function
02468-8-6-4-2-1010-500500
The domain of the function
The points at which the function is not precisely defined:
x1=0x_{1} = 0
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:
−17x2+11x=0\frac{- 17 x^{2} + 11}{x} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=−18717x_{1} = - \frac{\sqrt{187}}{17}
x2=18717x_{2} = \frac{\sqrt{187}}{17}
Numerical solution
x1=0.804399666539844x_{1} = 0.804399666539844
x2=−0.804399666539844x_{2} = -0.804399666539844
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to (11 - 17*x^2)/x.
−17⋅02+110\frac{- 17 \cdot 0^{2} + 11}{0}
The result:
f(0)=∞~f{\left(0 \right)} = \tilde{\infty}
sof doesn't intersect Y
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
−34−−17x2+11x2=0-34 - \frac{- 17 x^{2} + 11}{x^{2}} = 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
2⋅(17−17x2−11x2)x=0\frac{2 \cdot \left(17 - \frac{17 x^{2} - 11}{x^{2}}\right)}{x} = 0
Solve this equation
Solutions are not found,
maybe, the function has no inflections
Vertical asymptotes
Have:
x1=0x_{1} = 0
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞(−17x2+11x)=∞\lim_{x \to -\infty}\left(\frac{- 17 x^{2} + 11}{x}\right) = \infty
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡x→∞(−17x2+11x)=−∞\lim_{x \to \infty}\left(\frac{- 17 x^{2} + 11}{x}\right) = -\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 (11 - 17*x^2)/x, divided by x at x->+oo and x ->-oo
lim⁡x→−∞(−17x2+11x2)=−17\lim_{x \to -\infty}\left(\frac{- 17 x^{2} + 11}{x^{2}}\right) = -17
Let's take the limit
so,
inclined asymptote equation on the left:
y=−17xy = - 17 x
lim⁡x→∞(−17x2+11x2)=−17\lim_{x \to \infty}\left(\frac{- 17 x^{2} + 11}{x^{2}}\right) = -17
Let's take the limit
so,
inclined asymptote equation on the right:
y=−17xy = - 17 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:
−17x2+11x=−−17x2+11x\frac{- 17 x^{2} + 11}{x} = - \frac{- 17 x^{2} + 11}{x}
- No
−17x2+11x=−17x2+11x\frac{- 17 x^{2} + 11}{x} = \frac{- 17 x^{2} + 11}{x}
- No
so, the function
not is
neither even, nor odd
The graph
Graphing y = (11-17x^2)/x
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