Mister Exam

Other calculators

Plotting a function graph/ 48-2*x

Graphing y = 48-2*x

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
f(x) = 48 - 2*x
f(x)=48−2xf{\left(x \right)} = 48 - 2 x 
f = 48 - 2*x
The graph of the function
02468-8-6-4-2-10100100
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:
48−2x=048 - 2 x = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=24x_{1} = 24
Numerical solution
x1=24x_{1} = 24
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to 48 - 2*x.
48−048 - 0
The result:
f(0)=48f{\left(0 \right)} = 48
The point:
(0, 48)
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
−2=0-2 = 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→−∞(48−2x)=∞\lim_{x \to -\infty}\left(48 - 2 x\right) = \infty
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡x→∞(48−2x)=−∞\lim_{x \to \infty}\left(48 - 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 48 - 2*x, divided by x at x->+oo and x ->-oo
lim⁡x→−∞(48−2xx)=−2\lim_{x \to -\infty}\left(\frac{48 - 2 x}{x}\right) = -2
Let's take the limit
so,
inclined asymptote equation on the left:
y=−2xy = - 2 x
lim⁡x→∞(48−2xx)=−2\lim_{x \to \infty}\left(\frac{48 - 2 x}{x}\right) = -2
Let's take the limit
so,
inclined asymptote equation on the right:
y=−2xy = - 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:
48−2x=2x+4848 - 2 x = 2 x + 48
- No
48−2x=−2x−4848 - 2 x = - 2 x - 48
- No
so, the function
not is
neither even, nor odd
    © Mister Exam – Calculator