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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.
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What is a piece-wise function?
for a piecewise function, the domain is broken into pieces, with a different rule defining the function for each piece
What is X2-4 divided by x2 plus 3x plus 2 continuous or discontinuous?
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.
What does the horizontal line tell you about a function?
If the function is a one-to-one function, therefore it has an inverse.
Can a one to one function not be a function?
"y = f(x) is a function if it passes the vertical line test. It is a 1-1 function if it passes both the vertical line test and the horizontal line test. " - In order to be a one-to-one function, it first has to BE a function and pass the vertical line test. For example, a relation on a graph like a circle that does not pass the vertical line test is not function nor one-to-one.
A relation in which each element of the domain is paired with exactly one element of the range?
A relation where each element of the domain is paired with only one element of the range is a one to one function. A one to one function may also be an onto function if all elements of the range are paired.
The greatest integer function and absolute value function are both examples of functions that can be defined?
piecewise
What is piecewise smooth function?
f is a piecewise smooth funtion on [a,b] if f and f ' are piecewise continuous on [a,b]
Describe the defining characteristics of piecewise functions?
A piecewise defined function is a function which is defined symbolically using two or more formulas
When finding the derivative of a point on a piecewise function does every function in the piecewise function need to be continuous and approach the same limit?
All differentiable functions need be continuous at least.
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.
Do you connect points for a piecewise function?
yes :D
What is a piecewise function whose graph resembles a set of stair steps?
One such function is [ Y = INT(x) ]. (Y is equal to the greatest integer in ' x ')
What is a piece-wise function?
for a piecewise function, the domain is broken into pieces, with a different rule defining the function for each piece
What does a solid dot mean on a piecewise function represent?
It could represent a point whose coordinates do satisfy the requirements of the function.
Write a equation for piecewise function?
slope 5/6 through (-18,6)
How do you graph and evaluate piecewise functions?
Graph each "piece" of the function separately, on the given domain.
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.
