What graph represents f (x) = x over the domain 3

Ex. 1) A piecewise function is usually defined by more than one formula: a fomula for each interval.

Example 1:

f (x) = - x if x < = 2

= x if x > 2

What the above says is that if x is smaller than or equal to 2, the formula for the function is f (x) = - x and if x is greater than 2, the formula is f (x) = x. It is also important to note that the domain of function f defined above is the set of all the real numbers since f is defined everywhere for all real numbers.

Example 2:

f (x) = 2 if x > - 3

= - 5 if x < - 3

The above function is constant and equal to 2 if x is greater than - 3. function f is also constant and equal to - 5 if x is less than - 3. It can be said that function f is piecewise constant. The domain of f given above is the set of all real numbers except - 3: if x = - 3 function f is undefined.

Example 3:

Functions involving absolute value are also a good example of piecewise functions.

f (x) = | x |

Using the definition of the absolute value, function f given above can be written

f (x) = x if x > = 0

= - x if x < 0

The domain of the above function is the set of all real numbers.