Mister Exam
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-
How to use it?
- Graphing y =:
- x^3-((x^4)/4)
- x^3+6*x^2+9*x+4
- -x^3+3x^2+9x-12
- x^3+4x
-
Identical expressions
- (-x)/ two + one
- ( minus x) divide by 2 plus 1
- ( minus x) divide by two plus one
- -x/2+1
- (-x) divide by 2+1
-
Similar expressions
- 2*log(x)-x/2+1
- (-x)/2-1
- 3*(log(3)(1-x/2))+1
- 2*(log(x)/log(10))-x/2+1
- (x)/2+1
- 2*lg(x)-x/2+1
- sqrt((9/16)-(x/2))+(1/8)
-
What you mean?
- (-x)/(2 + 1)
- -x/2 + 1
- (-x)/(2 + 1)
- -x/2 + 1
- -x/2 + 1
You entered:
(-x)/2+1
What you mean?
Graphing y = (-x)/2+1
The solution
You have entered
[src]
-x
f(x) = --- + 1
2
$$f{\left(x \right)} = \frac{\left(-1\right) x}{2} + 1$$
f = -x/2 + 1
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:
$$\frac{\left(-1\right) x}{2} + 1 = 0$$
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:
$$\frac{\left(-1\right) x}{2} + 1 = 0$$
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
$$- \frac{1}{2} = 0$$
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
$$- \frac{1}{2} = 0$$
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
$$\lim_{x \to -\infty}\left(\frac{\left(-1\right) x}{2} + 1\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) x}{2} + 1\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(\frac{\left(-1\right) x}{2} + 1\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) x}{2} + 1\right) = -\infty$$
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 -x/2 + 1, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\frac{\left(-1\right) x}{2} + 1}{x}\right) = - \frac{1}{2}$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = - \frac{x}{2}$$
$$\lim_{x \to \infty}\left(\frac{\frac{\left(-1\right) x}{2} + 1}{x}\right) = - \frac{1}{2}$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = - \frac{x}{2}$$
$$\lim_{x \to -\infty}\left(\frac{\frac{\left(-1\right) x}{2} + 1}{x}\right) = - \frac{1}{2}$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = - \frac{x}{2}$$
$$\lim_{x \to \infty}\left(\frac{\frac{\left(-1\right) x}{2} + 1}{x}\right) = - \frac{1}{2}$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = - \frac{x}{2}$$
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:
$$\frac{\left(-1\right) x}{2} + 1 = \frac{x}{2} + 1$$
- No
$$\frac{\left(-1\right) x}{2} + 1 = - \frac{x}{2} - 1$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\frac{\left(-1\right) x}{2} + 1 = \frac{x}{2} + 1$$
- No
$$\frac{\left(-1\right) x}{2} + 1 = - \frac{x}{2} - 1$$
- No
so, the function
not is
neither even, nor odd
The graph