Business Mathematics

all of you maybe already know about what is "Business mathematics"
but i will explain it again.

Business Mathematics is usually used by commercial enterprises. they used to record and manage business operations.The commercial organization use it in inventory management, marketing , accounting , sales forecasting and financial analysis.
Mathematics typically used includes elementary arithmetic, elementary algebra, statistic and  financial probability. it also use more advanced mathematics such as calculus , matrix algebra and  linear programming.




Symmetry

In this basic part of mathematics "symmetry", we will see that calculus is a great aid in graphing
not only because it helps determine the shape of a graph, but also provides powerful technique for determining whether or not a curve "wiggles" between point.
this is some example that related to symmetry graph

• y-axis symmetry

consider the graph of y = x²
the portion to the left of the y-axis  is the reflection through the y-axis
of that portion to the right of the y-axis .

so a graph is symmetric about the y-axis if and only if (-x,y) lies on the graph when (a,b) does

• x-axis symmetry

 in the other hand, the x-axis just like the y-axis
but the changes is in the y point
so a graph is symmetric about the x-axis if and only if (x,-y) lies on the graph when (x,y) does.

• Origin symmetry

this type maybe rather difficult , but actually its quite simply
for example from the picture above,
the graph whenever the point (x,y) lies on the graph,(-x,-y)also lies on it



actually there is some more symmetry type , but i like to move on to



Translations and Reflections

now we gonna learn another technique .
but this technique is not necessarily the preferred way. However ,some functions and their asociated graph occur so frequently that we find it worthwhile to learn it


to make it simply , this is how it works

equation
 y = f(x) + c   (shift c unit upward)
y = f(x) - c     (shift c unit downward)

y = f(x - c)      ( shift c unit to the right )
y = f(x + c )    (shift c unit to the left )

y = -f(x)       (reflect about x-axis)
y = f(-x)       (reflect about y-axis)

y = c f (x)  c>1 (vertically stretch away from x-axis by a factor of c )
y = c f (x)  c<1 (vertically shrink toward x-axis by a factor of c)

• Horizontal Translation

take this example from the graph
the blue line f(x+2) is on the left to make it move to the right we can use equation y = f(x-c)
so the result is the green line f(x). this techniques used the same way if you want to move the graph to the right . if you do , that makes the graph to be f(x-2)
the c unit to make ow far you want to move the graph
so if you want to make a far away little bit, you used the larger number and if you want to move it to the left
just simply lower the c  unit number


Thats its for now.. thank you for seeing my blogs
see ya