Mister Exam
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-
How to use it?
- Graphing y =:
- (x^2-4)/(2x+5)
- x^2+3x-10
-
(x^2+3)/(x-1)
- x^2-10x+27
- Integral of d{x}:
-
-2x+4
-
Identical expressions
- -2x+ four
- minus 2x plus 4
- minus 2x plus four
-
Similar expressions
- (x-2)*(((x+4)/x)^2)
- x^2-2*x+4
- -2x-4
- (x-2)*(x+4)
- log(-x^2-2x)+(4-x)^1/2
- 2x+4
- 3*x-(2*x+4)/(x^2-2*x-8)
Graphing y = -2x+4
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:
$$4 - 2 x = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 2$$
Numerical solution
$$x_{1} = 2$$
so we need to solve the equation:
$$4 - 2 x = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 2$$
Numerical solution
$$x_{1} = 2$$
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
$$\lim_{x \to -\infty}\left(4 - 2 x\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(4 - 2 x\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(4 - 2 x\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(4 - 2 x\right) = -\infty$$
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 + 4, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{4 - 2 x}{x}\right) = -2$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = - 2 x$$
$$\lim_{x \to \infty}\left(\frac{4 - 2 x}{x}\right) = -2$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = - 2 x$$
$$\lim_{x \to -\infty}\left(\frac{4 - 2 x}{x}\right) = -2$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = - 2 x$$
$$\lim_{x \to \infty}\left(\frac{4 - 2 x}{x}\right) = -2$$
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:
$$4 - 2 x = 2 x + 4$$
- No
$$4 - 2 x = - 2 x - 4$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$4 - 2 x = 2 x + 4$$
- No
$$4 - 2 x = - 2 x - 4$$
- No
so, the function
not is
neither even, nor odd