Mister Exam

Other calculators

Plotting a function graph/ x/2+1

Graphing y = x/2+1

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
       x    
f(x) = - + 1
       2
f(x)=x2+1f{\left(x \right)} = \frac{x}{2} + 1 
f = x/2 + 1
The graph of the function
02468-8-6-4-2-1010-1010
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:
x2+1=0\frac{x}{2} + 1 = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=−2x_{1} = -2
Numerical solution
x1=−2x_{1} = -2
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to x/2 + 1.
02+1\frac{0}{2} + 1
The result:
f(0)=1f{\left(0 \right)} = 1
The point:
(0, 1)
Extrema of the function
In order to find the extrema, we need to solve the equation
ddxf(x)=0\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:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
the first derivative
12=0\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
d2dx2f(x)=0\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:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
the second derivative
0=00 = 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→−∞(x2+1)=−∞\lim_{x \to -\infty}\left(\frac{x}{2} + 1\right) = -\infty
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡x→∞(x2+1)=∞\lim_{x \to \infty}\left(\frac{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→−∞(x2+1x)=12\lim_{x \to -\infty}\left(\frac{\frac{x}{2} + 1}{x}\right) = \frac{1}{2}
Let's take the limit
so,
inclined asymptote equation on the left:
y=x2y = \frac{x}{2}
lim⁡x→∞(x2+1x)=12\lim_{x \to \infty}\left(\frac{\frac{x}{2} + 1}{x}\right) = \frac{1}{2}
Let's take the limit
so,
inclined asymptote equation on the right:
y=x2y = \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:
x2+1=1−x2\frac{x}{2} + 1 = 1 - \frac{x}{2}
- No
x2+1=x2−1\frac{x}{2} + 1 = \frac{x}{2} - 1
- No
so, the function
not is
neither even, nor odd
    © Mister Exam – Calculator