1) Write an equation of the line whose slope is 3 and ...
Hon Alg 2: Unit 1
Number Lines and Interval Notation
Interval Notation: Rather than writing out inequalities to describe the range or domain of values we use brackets and parentheses.
Parentheses “(“ and “)” are like less than “” statements.
Brackets “[“ and “]” are like less than or equal to “” statements.
Infinity “∞”
• To show that numbers will always get larger we use positive infinity with a parentheses “∞)”
• To show the numbers will always get smaller we use negative infinity with parentheses “( -∞”
EXAMPLES: Each number line is not drawn to scale.
1. _______________________________
2. _______________________________
3. _______________________________
4. _______________________________
5. _______________________________
Union “U”: unifies different sections of a number line together as an overall answer
6. ___________________________________
7. ___________________________________
8. ___________________________________
9. ___________________________________
10. ___________________________________
GRAPH INTERPRETATION WITH INTERVAL NOTATION
• Intervals represent the x-values (domain) of a graph, while you are often describing the y-values (range) of the points.
• Undefined “Ø” and Zero “0” y-value are important and specifically listed on the number line.
• The remaining number line describe where the graph has positive or negative y-values.
EXAMPLE #1:
1. What x-values give zero y-values?
2. What x-values give undefined y-values?
3. Write interval notation for x-values when the graph is …
3a. negative.
3b. positive.
3c. greater than or equal to zero.
3d. less than or equal to zero.
EXAMPLE #2:
1. What x-values give zero y-values?
2. What x-values give undefined y-values?
3. Write interval notation for x-values when the graph is …
3a. negative.
3b. positive.
3c. greater than or equal to zero.
3d. less than or equal to zero.
EXAMPLE #3:
1. Draw your own number line
Interpretation of the graph.
2. Write interval notation for x-values when the graph is …
2a. negative.
2b. positive.
EXAMPLE #4: Draw your own number line interpretation of the graph.
Write interval notation for x-values when the graph is …
a. negative.
b. positive.
EXAMPLE #5: Draw your own number line interpretation of the graph.
3. Write interval notation for x-values when the graph is …
3a. negative.
3b. positive.
3c. greater than or equal to zero.
3d. less than or equal to zero.
How can you determine a number line statement from an equation without graphing?
Step 1: Find all the zeros and undefined x-values for the equation.
Step 2: Try any x-value between consecutive zeros and/or undefined values to determine if the y-values are positive or negative in that region.
Example: y = (x + 4) (x – 6) (x +1)
• Why do you think -4, -1, and 6 are given in the number line as zeros?
PRACTICE: Consider why you think the given values are zeros or undefined?
1) y = 3(x + 7) (x – 2) (x – 5)
2) [pic]
3) y = (2x – 1) (x – 5) (x + 4) (x – 3)
4) [pic]
5) [pic]
Additional Practice: For each equation, make a complete number line statement.
1) y = (x + 5) (x – 7)
2) [pic]
3) y = (x + 3) (x + 6) (x – 2)
4) [pic]
5) [pic]
-----------------------
8
-4
-3
2
5
-7
5
-5
3
7
-1
-6
-3
4
9
7
10
12
-8
-9
-2
x-values
y-values
Number
Line5FG¹ÄÛäìø
* ? B C H ` c d t *[pic]CJaJhtp®h{ í>*[pic]CJaJhtp®hL,
CJaJh˜=?h{ í5?CJaJhtp®h{ íCJ
Ø
0
pos
neg
pos
pos
0
Ø
neg
5
-2
-6
11
Ø
0
0
neg
pos
neg
pos
neg
-9
0
-5
7
0
(-6, 3)
(-4, 0)
(0, -5)
(3, 0)
(5, -5)
(8, -5)
(10, 0)
2
4
6
8
10
14
16
-8
-4
-2
-6
1
2
3
4
5
7
8
-4
-2
-1
-3
6
0
-4
0
-1
0
6
0
0
0
2
5
-7
0
0
Ø
3
-2
0
0
0
0
0
-4
1/2
3
5
0
Ø
Ø
4
-1
6
Ø
0
0
0
-3
3
-9
2
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