y = x3
After translating 4 units left and 7 units down, this function would become:
y = (x+4)3-7
In single-variable mathematical functions, vertical translations are always achieved by simply adding or subtracting a number constant from the original function. Addition causes upward shift, subtraction causes downward shift.
Horizontal translations for simple functions are achieved by adding or subtracting number constants within the argument of the function in question. Addition causes leftward shift, subtraction causes rightward shift.
Vertical translations are easy to comprehend, horizontal translations are not always so easy. Some more examples:
y = sin(x) shifted pi units to the left is y = sin(x+(pi)). [this is also equal to y = cos(x)]
y = ln(x) shifted 5 units right is y = ln(x-5)
Take note: for more complex functions or polynomials not in vertex form, it is not always so simple. For example, a function like:
y = ln(sin(x)-cos(x))3
cannot have horizontal shifts so easily applied to it. Vertical shifting is still the same for any function regardless of complexity, so this function could still be vertically shifted by adding or subtracting number constants. I don't know off the top of my head how exactly to precisely shift this function horizontally, but I would recommend messing around on a graphing calculator to really gain a good knowledge of how changing certain parts of functions affects their appearance.
It is a hyperbola, it is in quadrants I and II
The minimum is the vertex which in this case is 0,0 or the origin. There isn't a maximum.....
y = 1/x
x2
parent element
Y=x
y = b^x
parent element
No, the parent in the nuclear equation is not always radioactive. For example, the following reaction shows a neutron capture by 23Na, which is not radioactive. 1123Na + 01n --> 1124Na where 01n is a neutron.
how would the court know?
You could put the equation in slope-intercept form or in parent linear function or even make a table of values.
if you need to reflect a 2-d object on a graph over its parent linear function then do as follows: (x,y) --> (-y,-x) hope that helps
Yes,life insurance can be obtained by any one for anyone.Its kinda sad.
A passport cannot be obtained without the signature of the other parent.
weather rock, gravel ,sand, silt, clay .these are obtained from the parent material the rock from which the soil is derived