Mister Exam
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-
How to use it?
- Graphing y =:
- x^3+x^2-x+1
- -x^2+4x
- x^2+2x-4
- x^2-2x-8
- Derivative of:
-
(2x+3)
- Integral of d{x}:
-
(2x+3)
-
Identical expressions
- (2x+ three)
- (2x plus 3)
- (2x plus three)
- 2x+3
-
Similar expressions
- (2x-3)
- sin(2*x+3)^(2)
- |2*x+3|/(2*x+3)
- (x^2-2*x+3)/(x-1)
- -x^2+2*x+3
Graphing y = (2x+3)
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:
$$2 x + 3 = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = - \frac{3}{2}$$
Numerical solution
$$x_{1} = -1.5$$
so we need to solve the equation:
$$2 x + 3 = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = - \frac{3}{2}$$
Numerical solution
$$x_{1} = -1.5$$
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
$$\lim_{x \to -\infty}\left(2 x + 3\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(2 x + 3\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(2 x + 3\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(2 x + 3\right) = \infty$$
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 + 3, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{2 x + 3}{x}\right) = 2$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = 2 x$$
$$\lim_{x \to \infty}\left(\frac{2 x + 3}{x}\right) = 2$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = 2 x$$
$$\lim_{x \to -\infty}\left(\frac{2 x + 3}{x}\right) = 2$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = 2 x$$
$$\lim_{x \to \infty}\left(\frac{2 x + 3}{x}\right) = 2$$
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:
$$2 x + 3 = 3 - 2 x$$
- No
$$2 x + 3 = 2 x - 3$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$2 x + 3 = 3 - 2 x$$
- No
$$2 x + 3 = 2 x - 3$$
- No
so, the function
not is
neither even, nor odd