Download 1) Write an equation of the line whose slope is 3 and whose y

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 “<” or greater than “>” statements.
Brackets “[“ and “]” are like less than or equal to “<” or greater 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.
8
1. _______________________________
-4
2. _______________________________
-3
2
3. _______________________________
-7
5
4. _______________________________
5. _______________________________
Union “U”: unifies different sections of a number line together as an overall answer
-1
-6
6. ___________________________________
-3
10
4
7. ___________________________________
8. ___________________________________
7
5
9
12
-5
-8
9. ___________________________________
-9
10. ___________________________________
-2
3
7
GRAPH INTERPRETATION WITH INTERVAL NOTATION
 Intervals represent the x-values (domain) of a graph, while
y-values
Number
you are often describing the y-values (range) of the points.
Line
x-values
 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:
Ø pos 0
pos
-6
neg
-2
1. What x-values give zero y-values?
0
pos
5
Ø
neg
11
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.
EXAMPLE #2:
3d. less than or equal to zero.
0
neg
-9
1. What x-values give zero y-values?
pos
0
neg
-5
Ø
neg
0
0
pos
7
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.
EXAMPLE #3:
1. Draw your own number line
Interpretation of the graph.
3d. less than or equal to zero.
(-6, 3)
(-4, 0)
(3, 0)
(0, -5)
2. Write interval notation for x-values when the graph is …
2a. negative.
2b. positive.
(10, 0)
(5, -5) (8, -5)
EXAMPLE #4: Draw your own number line interpretation of the graph.
-8
-6
-4
2
-2
4
6
8
14 16
10
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.
-4 -3 -2
-1
1
2
3
4
5
6
7 8
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 yvalues 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?
0
0
0
-4
-1
6
PRACTICE: Consider why you think the given values are zeros or undefined?
1) y = 3(x + 7) (x – 2) (x – 5)
0
0
0
-7
2) y 
2
5
( x  2)( x  3)
x
0
Ø
0
-2
0
3
3) y = (2x – 1) (x – 5) (x + 4) (x – 3)
0
0
1
-4
4) y 
5) y 
/2
0
0
3
5
( x  4)( x  6)
( x  6)( x  1)
( x  3)( x  3)( x  9)
( x  2)
0
Ø
0
Ø
-1
4
6
Ø
0
0
2
-9
-3
3
Additional Practice: For each equation, make a complete number line statement.
1) y = (x + 5) (x – 7)
( x  3)( x  1)
4) y 
( x  3)( x  6)
2) y 
( x  1)( x  5)
( x  2)
5) y 
3) y = (x + 3) (x + 6) (x – 2)
( x  4)( x  2)( x  1)
x ( x  4)