Mister Exam

# Graphing y = y=-5/12x+11

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### The solution

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         5*x
f(x) = - --- + 11
12     
$$f{\left(x \right)} = 11 - \frac{5 x}{12}$$
f = 11 - 5*x/12
The graph of the function
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:
$$11 - \frac{5 x}{12} = 0$$
Solve this equation
The points of intersection with the axis X:

Analytical solution
$$x_{1} = \frac{132}{5}$$
Numerical solution
$$x_{1} = 26.4$$
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to -5*x/12 + 11.
$$11 - 0$$
The result:
$$f{\left(0 \right)} = 11$$
The point:
(0, 11)
Extrema of the function
In order to find the extrema, we need to solve the equation
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} =$$
the first derivative
$$- \frac{5}{12} = 0$$
Solve this equation
function may have no extrema
Inflection points
Let's find the inflection points, we'll need to solve the equation for this
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} =$$
the second derivative
$$0 = 0$$
Solve this equation
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
$$\lim_{x \to -\infty}\left(11 - \frac{5 x}{12}\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(11 - \frac{5 x}{12}\right) = -\infty$$
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 -5*x/12 + 11, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{11 - \frac{5 x}{12}}{x}\right) = - \frac{5}{12}$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = - \frac{5 x}{12}$$
$$\lim_{x \to \infty}\left(\frac{11 - \frac{5 x}{12}}{x}\right) = - \frac{5}{12}$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = - \frac{5 x}{12}$$
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:
$$11 - \frac{5 x}{12} = \frac{5 x}{12} + 11$$
- No
$$11 - \frac{5 x}{12} = - \frac{5 x}{12} - 11$$
- No
so, the function
not is
neither even, nor odd