FINDING DOMAIN AND RANGE OF A PIECEWISE FUNCTION

Graph each of the following piecewise functions neatly and provide the requested information.

Problem 1 :

Solution :

Second piece :

y = 3

Since it is linear function, it should create a horizontal line. 

Domain = (-∞, -1), (0, 2) U [4, ∞)

Range = (-∞,∞)

Problem 2 :

First piece :

y = x²

Since it is quadratic function, it must be a parabola, opens up.

Second piece :

y = √x

It is a square root function, it is not defined for the negative values.  

Domain = (-∞, ∞)

Range = (0,∞)

Problem 3 :

First piece :

y = √(x - 1)

It is a square root function, it is not defined for the negative values.

Points are (1, 0) (2, 1) (3, 2) and (4, 3).

Domain = (-∞, -1] U [1,∞)

Range = (-∞, ∞)

Problem 4 :

Domain = (-∞, ∞)

Range = (-∞, -4) U (-1,∞)

Problem 5 :

Solution :

First piece :

y = |x|

Since it is absolute value function, it will be in the shape of V.

vertex will be at (0, 0) and opens up.

Domain = (-∞, ∞)

Range = (-∞,∞)

Find the domain and range of the piecewise function given below.

Problem 6 :

Solution :

Domain = [-5, 5]

Range = [-2, 4]

Problem 7 :

Solution :

Domain = (-∞, ∞)

Range = [-2, ∞)