For the piecewise function find the values calculator

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Find the domain and range of a function with Wolfram|Alpha
More than just an online function properties finder
Tips for entering queries
VIEW ALL CALCULATORS
What is domain and range?
11.14. Piece-wise Functions

Find the domain and range of a function with Wolfram|Alpha

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More than just an online function properties finder

Wolfram|Alpha is a great tool for finding the domain and range of a function. It also shows plots of the function and illustrates the domain and range on a number line to enhance your mathematical intuition.

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Domain and range »

Tips for entering queries

Enter your queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask for the domain and range.

domain of log(x)
(x^2+1)/(x^2-1) domain
find the domain of 1/(e^(1/x)-1)

function domain: square root of cos(x)
log(1-x^2) domain
range of arccot(x)

View more examples »

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What is domain and range?

The domain of a function, , is most commonly defined as the set of values for which a function is defined. For example, a function that is defined for real values in has domain , and is sometimes said to be "a function over the reals." The set of values to which is sent by the function is called the range.

Informally, if a function is defined on some set, then we call that set the domain. The values taken by the function are collectively referred to as the range. For example, the function takes the reals (domain) to the non-negative reals (range). The sine function takes the reals (domain) to the closed interval (range). (Both of these functions can be extended so that their domains are the complex numbers, and the ranges change as well.)

11.14. Piece-wise Functions

A piece-wise function is defined as a sequence of intervals and each interval is a subset of the domain of the function. Some examples of piece-wise functions are:

Sketching a piece-wise function means sketching the graphs of several functions with applied domains. Use the following steps in Graph mode:

1) Enter the equation for the first interval.
    The default domain is from -∞ to +∞.
    Change the domain to the equation's given interval.
    Tap the down-arrow on the left of the input field to be able to change the equation's domain.

2) Enter the equation for the second interval.
Change the default domain based on the given second interval.

3) Use the same procedure for each of the following intervals.

Examples
Sketch the graph of each piece-wise function below.

Solutions
1) Type x - 5.
    Tap the down-arrow on the left of the input field.
   Keep -∞ as the lower bound but change the upper bound from ∞ to 2.
    Hit the enter key three times.

    Type x^2 + 2.
    Tap the down-arrow on the left of the input field.
Change the lower bound from -∞ to 2 and keep the upper bound at ∞.
   Hit the enter key three times.

2) Enter |2x + 1| by using the absolute value key |x|. It should appear as abs(2x + 1).
Tap the down-arrow on the left of the input field.
Change the lower bound from -∞ to 0 and keep the upper bound at ∞.
Hit the enter key three times.

    Enter (x - 2) ^ 2.
    Tap the down-arrow on the left of the input field.
   Keep the lower bound at -∞ but change the upper bound from ∞ to 0.
    Hit the enter key three times.

3) Enter 3x + 2.
Tap the down-arrow on the left of the input field.
Change the lower bound from -∞ to -1 and keep the upper bound at ∞.
Hit the enter key three times.

Plot the point (-1, 3) by typing [-1, 3].
Hit the enter key.

    Enter x^3 + x - 1.
    Tap the down-arrow on the left of the input field.
   Keep the lower bound at -∞ and change the upper bound from ∞ to -1.
   Hit the enter key three times.