Mister Exam
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- The intersection points of functions
-
How to use it?
- Graphing y =:
- -x^2+6x-3
- x^2-2x+8
- (x+5)^2
- x^4+4
- Derivative of:
-
2x-5
- Integral of d{x}:
-
2x-5
-
Identical expressions
- 2x- five
- 2x minus 5
- 2x minus five
-
Similar expressions
- 2x+5
- log(2)(x-5)
- x^2+2*x-5
- -sin(10*x)-5*sin(2*x)-5*sin(4*x)/2-5*sin(6*x)/3-5*sin(8*x)/4+2*(pi*(-3)+5*pi^1)/pi
Graphing y = 2x-5
The solution
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:
$$2 x - 5 = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = \frac{5}{2}$$
Numerical solution
$$x_{1} = 2.5$$
so we need to solve the equation:
$$2 x - 5 = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = \frac{5}{2}$$
Numerical solution
$$x_{1} = 2.5$$
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
$$2 = 0$$
Solve this equation
Solutions are not found,
function may have no extrema
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(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
$$2 = 0$$
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
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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
Solutions are not found,
maybe, the function has no inflections
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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
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
$$\lim_{x \to -\infty}\left(2 x - 5\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(2 x - 5\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(2 x - 5\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(2 x - 5\right) = \infty$$
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 2*x - 5, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{2 x - 5}{x}\right) = 2$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = 2 x$$
$$\lim_{x \to \infty}\left(\frac{2 x - 5}{x}\right) = 2$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = 2 x$$
$$\lim_{x \to -\infty}\left(\frac{2 x - 5}{x}\right) = 2$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = 2 x$$
$$\lim_{x \to \infty}\left(\frac{2 x - 5}{x}\right) = 2$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = 2 x$$
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:
$$2 x - 5 = - 2 x - 5$$
- No
$$2 x - 5 = 2 x + 5$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$2 x - 5 = - 2 x - 5$$
- No
$$2 x - 5 = 2 x + 5$$
- No
so, the function
not is
neither even, nor odd