Let's observe the given step function.

f (x) = ⎩ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎧ - 2, - 1, 0, 1, if - 6 \leq x < - 5 if - 5 \leq x < - 3 if - 3 \leq x < - 2 if - 2 \leq x < 0

To think about how to draw the graph, let's look at the first piece of the function. The restriction on the domain tells us that

f (x)

equals

- 2

when

x

is greater than or equal to

- 6

and less than

- 5 .

f (x) = - 2 if - 6 \leq x < - 5

To graph this, we draw a horizontal line at

y = - 2

extending from

x = - 6

to

x = - 5 .

To indicate that

x = - 6

is contained in the solution set, we place a closed circle at that point.

x = - 5

is not contained in the solution set of this piece, which we indicate with an open circle.

Following a similar process, we can graph the other pieces of the function.

Now that we have graphed the function, we can describe its domain and range.

The domain of a function is the set of

x -

values for which the function is defined. From the graph (and the function rule), we can see that

x

can equal any value from

- 6

to

0,

not including

0 .

- 6 \leq x < 0

The range of a function is the set of

y -

values for which the function is defined. From the graph (and the function rule), we can see that

y

can only equal

- 2, - 1, 0,

and

1 .

{- 2, - 1, 0, 1}

Exercise