Download 2. Set and Interval Notation Activity

Name ___________________________________ Student ID Number _____________________
Group Name ____________________________________________________________________
Group Members _________________________________________________________________
Set and Interval Notation
1. Determine whether or not each listed value is an element (member) of the set described by the
graph of set Y below. Fill in the blanks with the appropriate symbol, either ϵ (meaning “is an
element of the set”) or ϵ (meaning “is NOT an element of the set”).
-5 -4 -3 -2 -1
0
1
2
3
4
5
3 ____ Y
4 ____ Y
10 ____ Y
½ ____ Y
0 ____ Y
- ½ ____ Y
¾ ____ Y
-20 ____ Y
5 ____ Y
8
3
____ Y
-1 ____ Y
-100 ____ Y
2. Determine whether or not each listed value is an element (member) of the set described by the
graph of set Z below. Fill in the blanks with the appropriate symbol, either ϵ (meaning “is an
element of the set”) or ϵ (meaning “is NOT an element of the set”).
-5 -4 -3 -2 -1
0
1
2
3
4
5
3 ____ Z
4 ____ Z
10 ____ Z
½ ____ Z
0 ____ Z
- ½ ____ Z
¾ ____ Z
-20 ____ Z
5 ____ Z
8
3
____ Z
-1 ____ Z
-100 ____ Z
Using set-builder notation, we can describe the intervals on page 1. The graph in problem 1
describes the set:
{𝑥𝑥|𝑥𝑥 < 4}
The graph in problem 2 describes the set:
{𝑥𝑥| − 1 < 𝑥𝑥 ≤ 4}
Now let’s take a look at interval notation. Using interval notation to represent the interval described
by the graph in problem 1, we have:
(−∞, 4).
The interval described by the graph in problem 2 is:
(−1, 4].
3. Using the examples above, list what you notice about similarities and/or differences in setbuilder notation and interval notation.
4. What is the difference between ≤ and <?
5. What is the difference between using [ and (?
6. Write the set described by each graph in set-builder notation, interval notation, AND write the
set in words.
a.
-5 -4 -3 -2 -1
0
1
2
3
4
5
Set-builder notation: _________________________________________________
Interval notation: ____________________________________________________
Words: ____________________________________________________________
b.
-5 -4 -3 -2 -1
0
1
2
3
4
5
Set-builder notation: _________________________________________________
Interval notation: ____________________________________________________
Words: ____________________________________________________________
c.
-5 -4 -3 -2 -1
0
1
2
3
4
5
Set-builder notation: _________________________________________________
Interval notation: ____________________________________________________
Words: ____________________________________________________________
d.
-5 -4 -3 -2 -1
0
1
2
3
4
5
Set-builder notation: _________________________________________________
Interval notation: ____________________________________________________
Words: ____________________________________________________________
e.
-5 -4 -3 -2 -1
0
1
2
3
4
5
Set-builder notation: _________________________________________________
Interval notation: ____________________________________________________
Words: ____________________________________________________________
f. What are the basic “rules” for using set-builder notation?
g. What are the basic “rules” for using interval notation?
Distance and Midpoint Formulas
Given two points on a Cartesian Plane, how would you determine the distance between them? Let’s
look at an example:
y
4
(-2, 3)
2
5 x
5
(1, -1)
2
4
Start by connecting the two points. Do you know the length of that line segment?
y
4
(-2, 3)
2
5 x
5
(1, -1)
2
4
Does this give you any ideas? What if we make a triangle? How would this help us determine the
distance between the original two points?
y
4
(-2, 3)
2
5 x
5
(1, -1)
2
4
7. What kind of triangle did we make? _____________________________________________
8. What theorem do you know that can help you determine the length of the hypotenuse of this
triangle? _______________________________________
9. Showing your work below, determine the distance between the points (−2, 3) and (1, −1).
10. Determine the distance between the points (−2, 2) and (10, −3). Graph the points below to help
you.
y 12
10
8
6
4
2
10
5
5
10
x
2
4
6
8
10
12
11. Write the Distance Formula using the general points (𝑥𝑥1 , 𝑦𝑦1 ) and (𝑥𝑥2 , 𝑦𝑦2 ).
𝑑𝑑 =
12. Next, we will find the midpoint of some line segments. If we are given two numbers on a number
line, we can easily determine the midpoint. How would you determine the midpoint between -3
and 4? Use the number line to help you describe your process below.
6
4
-5
-6
2
-4
-3
2
-2
-1
0
1
2
4
3
4
6
5
6
13. State a formula for determining the midpoint between x and y.
𝑚𝑚 =
14. How do you think you could expand the process you described above for points in the Cartesian
Plane?
15. Could you find the midpoint of (−4, 1) and (3, 5) using the method you described in number
14? Attempt to do so before turning to page 8. You will be graded on effort for this problem, not
correctness. Think and write down your thoughts along with any necessary work!
y
6
(3, 5)
4
2
(-4, 1)
5
5
2
4
6
x
16. If you already found the midpoint, great! If not, use the picture below to attempt to determine the
midpoint. Determine the lengths of each of the dotted lines. Can you find the midpoint now?
y
6
(3, 5)
4
2
(-4, 1)
5
5
x
2
4
6
17. Write the Midpoint Formula using the general points (𝑥𝑥1 , 𝑦𝑦1 ) and (𝑥𝑥2 , 𝑦𝑦2 ).
𝑀𝑀 =