Question

Graph each piecewise function. Then Identify the properties.

Answer 1

Answer:

The domain is:

x: (-∞, 0] U (0, ∞)

The range is

y: [0, ∞)

Step-by-step explanation:

These types of functions are known as piecewise functions. It has two pieces of functions, you must graph both pieces for each interval.

First, graph:

y = -x        for x from -∞ to x = 0

Note that y = -x is the equation of a negative slope line = -1 that passes through the origin

Second, graph:

y = x       for x from x = 0 to ∞

Note that y = x is the equation of a positive slope line = 1 that passes through the origin.

The graph of this function is shown in the attached image. Note that it matches the absolute value graph of x.

y = | x |

In this function y it is always positive, and x can be any real number.

Therefore the domain is:

x: (-∞, 0] U (0,∞)

The range is:

y: [0, ∞)