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Graphing y = -11/2*x+25

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The graph:

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Intersection points:

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Piecewise:

The solution

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         11*x     
f(x) = - ---- + 25
          2       
f(x)=2511x2f{\left(x \right)} = 25 - \frac{11 x}{2}
f = 25 - 11*x/2
The graph of the function
02468-8-6-4-2-1010-100100
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:
2511x2=025 - \frac{11 x}{2} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=5011x_{1} = \frac{50}{11}
Numerical solution
x1=4.54545454545454x_{1} = 4.54545454545454
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to -11*x/2 + 25.
25025 - 0
The result:
f(0)=25f{\left(0 \right)} = 25
The point:
(0, 25)
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
112=0- \frac{11}{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
0=00 = 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
limx(2511x2)=\lim_{x \to -\infty}\left(25 - \frac{11 x}{2}\right) = \infty
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
limx(2511x2)=\lim_{x \to \infty}\left(25 - \frac{11 x}{2}\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*x/2 + 25, divided by x at x->+oo and x ->-oo
limx(2511x2x)=112\lim_{x \to -\infty}\left(\frac{25 - \frac{11 x}{2}}{x}\right) = - \frac{11}{2}
Let's take the limit
so,
inclined asymptote equation on the left:
y=11x2y = - \frac{11 x}{2}
limx(2511x2x)=112\lim_{x \to \infty}\left(\frac{25 - \frac{11 x}{2}}{x}\right) = - \frac{11}{2}
Let's take the limit
so,
inclined asymptote equation on the right:
y=11x2y = - \frac{11 x}{2}
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:
2511x2=11x2+2525 - \frac{11 x}{2} = \frac{11 x}{2} + 25
- No
2511x2=11x22525 - \frac{11 x}{2} = - \frac{11 x}{2} - 25
- No
so, the function
not is
neither even, nor odd