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How are piecewise functions related to step functions and absolute value functions?
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.
Describe the defining characteristics of piecewise functions?
A piecewise defined function is a function which is defined symbolically using two or more formulas
Can you please show that first derivation is piecewise continuous?
Assuming you mean "derivative", I believe it really depends on the function. In the general case, there is no guarantee that the first derivative is piecewise continuous, or that it is even defined.
If an original expression is defined for all values of x you do not need to specify the absolute value in the simplified expression.?
The assertion is not true. Consider the function f(x) =|x - 3|, which is the distance of x from the point 3. The function is defined for all x but the absolute value is required.
What are limits in maths?
Limits (or limiting values) are values that a function may approach (but not actually reach) as the argument of the function approaches some given value. The function is usually not defined for that particular value of the argument.
