Mister Exam
Other calculators
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- The intersection points of functions
-
How to use it?
- Graphing y =:
-
x^3-3x-1
- x^3-2x^2+x
- x^2-4x+6
-
x-(9/x)
-
Identical expressions
- sqrt(x- three)
- square root of (x minus 3)
- square root of (x minus three)
- √(x-3)
- sqrtx-3
-
Similar expressions
- sqrt(x+3)
- abs((sqrt(x)-3))
- sqrt(x)^-3*x+4
- ((2*sqrt(x)+3)/sqrt(x))-((3*sqrt(x))/x)-x+5
- tg(sqrt(x))-3x^2-5*sqrt(x)
- x*sqrt(x)-3*x+1
Graphing y = sqrt(x-3)
The solution
You have entered
[src]
_______ f(x) = \/ x - 3
$$f{\left(x \right)} = \sqrt{x - 3}$$
f = sqrt(x - 1*3)
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:
$$\sqrt{x - 3} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 3$$
Numerical solution
$$x_{1} = 3$$
so we need to solve the equation:
$$\sqrt{x - 3} = 0$$
Solve this equation
The points of intersection with the axis X:
Analytical solution
$$x_{1} = 3$$
Numerical solution
$$x_{1} = 3$$
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
$$\frac{1}{2 \sqrt{x - 3}} = 0$$
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
$$\frac{1}{2 \sqrt{x - 3}} = 0$$
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
$$- \frac{1}{4 \left(x - 3\right)^{\frac{3}{2}}} = 0$$
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
$$- \frac{1}{4 \left(x - 3\right)^{\frac{3}{2}}} = 0$$
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
$$\lim_{x \to -\infty} \sqrt{x - 3} = \infty i$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty} \sqrt{x - 3} = \infty$$
Let's take the limit
so,
horizontal asymptote on the right doesn’t exist
$$\lim_{x \to -\infty} \sqrt{x - 3} = \infty i$$
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
$$\lim_{x \to \infty} \sqrt{x - 3} = \infty$$
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 sqrt(x - 1*3), divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\sqrt{x - 3}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty}\left(\frac{\sqrt{x - 3}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
$$\lim_{x \to -\infty}\left(\frac{\sqrt{x - 3}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
$$\lim_{x \to \infty}\left(\frac{\sqrt{x - 3}}{x}\right) = 0$$
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
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:
$$\sqrt{x - 3} = \sqrt{- x - 3}$$
- No
$$\sqrt{x - 3} = - \sqrt{- x - 3}$$
- No
so, the function
not is
neither even, nor odd
So, check:
$$\sqrt{x - 3} = \sqrt{- x - 3}$$
- No
$$\sqrt{x - 3} = - \sqrt{- x - 3}$$
- No
so, the function
not is
neither even, nor odd