Answer:
Certainly! Let's graph the step function
�
(
�
)
=
∣
�
+
3
∣
f(x)=∣x+3∣ over the interval
−
2
≤
�
≤
2
−2≤x≤2.
The absolute value function
∣
�
+
3
∣
∣x+3∣ can be broken down into two cases based on the sign of
�
+
3
x+3:
When
�
+
3
≥
0
x+3≥0, i.e.,
�
≥
−
3
x≥−3, the function is
�
(
�
)
=
�
+
3
f(x)=x+3.
When
�
+
3
<
0
x+3<0, i.e.,
�
<
−
3
x<−3, the function is
�
(
�
)
=
−
(
�
+
3
)
f(x)=−(x+3).
Let's consider each case within the given interval:
For
�
≥
−
3
x≥−3:
�
(
�
)
=
�
+
3
f(x)=x+3
For
�
<
−
3
x<−3:
�
(
�
)
=
−
(
�
+
3
)
f(x)=−(x+3)
Now, let's plot these on the graph:
For
�
≥
−
3
x≥−3:
Draw the line
�
=
�
+
3
y=x+3 over the interval
−
2
≤
�
≤
2
−2≤x≤2.
This line starts at
(
−
3
,
0
)
(−3,0) and goes upwards with a slope of 1.
For
�
<
−
3
x<−3:
Draw the line
�
=
−
(
�
+
3
)
y=−(x+3) over the interval
−
2
≤
�
≤
2
−2≤x≤2.
This line starts at
(
−
5
,
0
)
(−5,0) and goes downwards with a slope of -1.
The graph will consist of two line segments. I recommend using graph paper or a graphing tool for a more accurate representation.
Explanation: