A piecewise function can be one-to-one, but it is not guaranteed to be. A function is considered one-to-one if each element in the domain maps to a unique element in the range. In the case of a piecewise function, it depends on the specific segments and how they are defined. If each segment of the piecewise function passes the horizontal line test, then the function is one-to-one.
The numerator function x2 - 4 and the denominator function x2 + 3x + 2 are both continuous functions of x for the entire x-axis. However, the quotient of these two functions is not continuous when the denominator function has the value of 0, because division by zero is not defined. The denominator function is 0 when x = -1 or -2. Therefore, the quotient function is not fully continuous over any intervals that include -1 or -2, but it is "piecewise continuous" over other intervals of the x-axis.
That's easy. Take any function that is defined on R except 0, then shift it 4.1 units to the right. To do a shift operation of a units, it is simply taking f(x - a) instead of f(x) So in this case, take f(x) = 1/x, a is 4.1 f(x - 4.1) = 1/ (x - 4.1) is exactly what you want. Also, there are other piecewise functions: f(x) = 1 if x < 4.1 and 0 if x > 4.1 not defined when x = 4.1
GetA is a math function and not a string function.
Differential equation is defined in the domain except at few points (may be consider the time domain ti ) may be (finite or countable) in the domain and a function or difference equation is defined at each ti in the domain. So, differential equation with the impulsive effects we call it as impulsive differential equation (IDE). The solutions of the differential equation is continuous in the domain. But the solutions of the IDE are piecewise continuous in the domain. This is due to the nature of impulsive system. Generally IDE have first order discontinuity. There are so many applications for IDE in practical life.
piecewise
f is a piecewise smooth funtion on [a,b] if f and f ' are piecewise continuous on [a,b]
A piecewise function can be one-to-one, but it is not guaranteed to be. A function is considered one-to-one if each element in the domain maps to a unique element in the range. In the case of a piecewise function, it depends on the specific segments and how they are defined. If each segment of the piecewise function passes the horizontal line test, then the function is one-to-one.
A piecewise defined function is a function which is defined symbolically using two or more formulas
All differentiable functions need be continuous at least.
A piecewise function is a function defined by two or more equations. A step functions is a piecewise function defined by a constant value over each part of its domain. You can write absolute value functions and step functions as piecewise functions so they're easier to graph.
yes :D
Piecewise <3
It could represent a point whose coordinates do satisfy the requirements of the function.
slope 5/6 through (-18,6)
Graph each "piece" of the function separately, on the given domain.
One such function is [ Y = INT(x) ]. (Y is equal to the greatest integer in ' x ')