Mister Exam

Other calculators

Plotting a function graph/ 3-5*(x+1)

Graphing y = 3-5*(x+1)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
f(x) = 3 - 5*(x + 1)
f(x)=3−5(x+1)f{\left(x \right)} = 3 - 5 \left(x + 1\right) 
f = 3 - 5*(x + 1)
The graph of the function
02468-8-6-4-2-1010-100100
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:
3−5(x+1)=03 - 5 \left(x + 1\right) = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=−25x_{1} = - \frac{2}{5}
Numerical solution
x1=−0.4x_{1} = -0.4
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to 3 - 5*(x + 1).
−5+3-5 + 3
The result:
f(0)=−2f{\left(0 \right)} = -2
The point:
(0, -2)
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
−5=0-5 = 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→−∞(3−5(x+1))=∞\lim_{x \to -\infty}\left(3 - 5 \left(x + 1\right)\right) = \infty
Let's take the limit
so,
horizontal asymptote on the left doesn’t exist
lim⁡x→∞(3−5(x+1))=−∞\lim_{x \to \infty}\left(3 - 5 \left(x + 1\right)\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 - 5*(x + 1), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(3−5(x+1)x)=−5\lim_{x \to -\infty}\left(\frac{3 - 5 \left(x + 1\right)}{x}\right) = -5
Let's take the limit
so,
inclined asymptote equation on the left:
y=−5xy = - 5 x
lim⁡x→∞(3−5(x+1)x)=−5\lim_{x \to \infty}\left(\frac{3 - 5 \left(x + 1\right)}{x}\right) = -5
Let's take the limit
so,
inclined asymptote equation on the right:
y=−5xy = - 5 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:
3−5(x+1)=5x−23 - 5 \left(x + 1\right) = 5 x - 2
- No
3−5(x+1)=2−5x3 - 5 \left(x + 1\right) = 2 - 5 x
- No
so, the function
not is
neither even, nor odd
    © Mister Exam – Calculator