Mister Exam
Other calculators
- Graph of implicit function
- Derivative Step by Step
- Integral Step by Step
- Graph of parametric function
- Graph in Polar Coordinates
- Surface defined parametrically
- Surface defined by equation
- Curve in 3D space defined parametrically
- Area between lines
- The intersection points of functions
-
How to use it?
- Graphing y =:
-
y=|x-2|-|x+1|+x-2
- -1/3x^3+4x
- x^4-4x^2+5
- x^3-x^4
- Integral of d{x}:
-
2*x+1
- Derivative of:
-
2*x+1
-
Identical expressions
- two *x+ one
- 2 multiply by x plus 1
- two multiply by x plus one
- 2x+1
-
Similar expressions
- (2x+1)^3
- log(1/2)(x+1)
- (2sin^(2)x)+2sin(2x)+1
- 2*x-1
- log1/2(x+1)
Graphing y = 2*x+1
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:
$$2 x + 1 = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = - \frac{1}{2}$$
Numerical solution
$$x_{1} = -0.5$$
so we need to solve the equation:
$$2 x + 1 = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = - \frac{1}{2}$$
Numerical solution
$$x_{1} = -0.5$$
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
$$\lim_{x \to -\infty}\left(2 x + 1\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(2 x + 1\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(2 x + 1\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(2 x + 1\right) = \infty$$
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 + 1, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{2 x + 1}{x}\right) = 2$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = 2 x$$
$$\lim_{x \to \infty}\left(\frac{2 x + 1}{x}\right) = 2$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = 2 x$$
$$\lim_{x \to -\infty}\left(\frac{2 x + 1}{x}\right) = 2$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = 2 x$$
$$\lim_{x \to \infty}\left(\frac{2 x + 1}{x}\right) = 2$$
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:
$$2 x + 1 = 1 - 2 x$$
- No
$$2 x + 1 = 2 x - 1$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$2 x + 1 = 1 - 2 x$$
- No
$$2 x + 1 = 2 x - 1$$
- No
so, the function
not is
neither even, nor odd