Practice: Interval Notation
Practice: Interval Notation
Use interval notation to describe the number(s) graphed on each number line.
1.
2.
3.
-6 -4 -2 0 2 4 6
-6 -4 -2 0 2 4 6
-6 -4 -2 0 2 4 6
4.
-6 -4 -2 0 2 4 6
5.
-6 -4 -2 0 2 4 6
6.
-6 -4 -2 0 2 4 6
New stuff! Union vs. Intersection
Union: the symbol Numbers that... ? belong in one set OR another ? are brought together
We could describe the numbers that belong to the interval (-5, -1] OR the interval (2, 4) through the notation (-5, -1] (2, 4). Its visual representation is below.
(-5, -1] (2, 4)
-6 -4 -2
02 4
6
Intersection: the symbol Numbers that... ? belong in one set AND another ? two sets share
We could describe the numbers that belong to the
interval (-3, 2) AND the interval [0, 5) through
the notation (-3, 2) [0, 5). A visualization of
the set is below.
(-3, 2)
-6 -4 -2 0 2 4 6
[0, 5)
-6 -4 -2 0 2 4 6 The overlapping area is
shaded. It shows which
numbers the two sets share.
(-3, 2) [0, 5)
-6 -4 -2 0 2 4 6
Describe the intervals on the number line using interval notation. You may need a or symbol.
7.
8.
-6 -4 -2
02 4
6
-6 -4 -2
02 4
6
Use interval notation to analyze each graph. 9. When is the graph above the x-axis?
4y
3
2
1
x
-4 -3 -2 --11 -2 -3 -4
12 34 5
10. When is the graph below the x-axis?
4y
3
2
1
x
-4 -3 -2 --11 -2 -3 -4
12 34 5
11. On what interval(s) is the graph below the x-axis?
4y
3
2
1
x
-4 -3 -2 --11 -2 -3 -4
12 34 5
12. On what interval(s) is the graph above the x-axis?
4y
3
2
1
x
-4 -3 -2 --11 -2 -3 -4
12 34 5
13. When is the graph above AND below the x-axis?
14. When is the graph above AND below the x-axis?
Create a graph that has the following characteristics.
15. The graph is above the x-axis on the interval 16. The graph is below the x-axis on the interval
(2, )
(-4, 0) (2, 5].
-6 -4 -2
02 4
6
-6 -4 -2
02 4
6
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