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Piecewise Functions

Piecewise Functions, a selection of answers from the Dr. Math archives.

What are Piecewise Functions?

I know piecewise functions are based on expressions between specific intervals, but I do not know how to describe this function family.

Determining Whether a Function is Continuous

How can you tell whether or not a function is continuous?

Graphing Piecewise Functions

I do not understand how to graph piecewise functions.

Piecewise Function

How do you graph the piecewise function?

Functions: Domain, Range, and Piecewise

What are piecewise functions? What are open and closed points? How do you figure out the domain and range of a function without graphing it on a calculator?

Continuity and Differentiability of Piecewise Function

What values of "a" and "b" will make this piecewise function continuous and differentiable?

Find a Function, Integrals

Suppose the graph of f has the formula f(x)=-x+1 for 0<=x<=1; x-1 for 1<x<=2 ...

Piecewise Notation and Absolute Value

How do I use piecewise notation to write x in terms of y for "y=2x+ abs(2-x)"?

Best Curve Fit

I have a series of points on a graph that form a piecewise equation that 'steps' down as x increases. I need to create an equation from these points that approximates values through the step, i.e. a natural log graph.

Differentiability, Intervals, Inflection Points of Piecewise Function

For what values of k and p will the function be continuous and differentiable? On what interval will it be increasing? Find all points of inflection.

Calculus of Piecewise Functions

Can I take the integral or derivative of a piecewise function like the floor function [u] or the absolute value function |u| and still notate it in concise form, |U| or [U]?