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

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download