Mister Exam
Other calculators
- Graph of implicit function
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- Integral Step by Step
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- 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 =:
- ((x^2+x-6)(x^2-2x-3))/(x^2-9)
- x/(x²-1)
-
|x+7|
- (x+5)^2
- Derivative of:
-
-3x
- Integral of d{x}:
-
-3x
- Canonical form:
- -3x
-
Identical expressions
- -3x
- minus 3x
-
Similar expressions
- (6x-18)/(x^2-3*x)
- 3x
- 5+4*x-3*x+6
Graphing y = -3x
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:
$$- 3 x = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 0$$
Numerical solution
$$x_{1} = 0$$
so we need to solve the equation:
$$- 3 x = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 0$$
Numerical solution
$$x_{1} = 0$$
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
$$-3 = 0$$
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
$$-3 = 0$$
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
$$\lim_{x \to -\infty}\left(- 3 x\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(- 3 x\right) = -\infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty}\left(- 3 x\right) = \infty$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty}\left(- 3 x\right) = -\infty$$
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 -3*x, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty} -3 = -3$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = - 3 x$$
$$\lim_{x \to \infty} -3 = -3$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = - 3 x$$
$$\lim_{x \to -\infty} -3 = -3$$
Let's take the limit
so,
inclined asymptote equation on the left:
$$y = - 3 x$$
$$\lim_{x \to \infty} -3 = -3$$
Let's take the limit
so,
inclined asymptote equation on the right:
$$y = - 3 x$$
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:
$$- 3 x = 3 x$$
- No
$$- 3 x = - 3 x$$
- Yes
so, the function
is
odd
So, check:
$$- 3 x = 3 x$$
- No
$$- 3 x = - 3 x$$
- Yes
so, the function
is
odd