Alg2X – UNIT 2



Alg2X – UNIT 2

Name__________________________________________ Period__________

If the directions state to EXPLAIN you need to string words together to form a sentence. Deductions for not following directions.

|DAY |TOPIC |ASSIGNMENT |

|1 |Domain, Range, Relations vs. Functions, Vertical Line Test (p. 48 #21,|1.6 pp. 47-48 #1-29 ODD, 31-33 (skip 5,11,21) 44, 46 |

| |31-37 if time) | |

|2 |Function notation, independent/dependentVariables, Graphing Functions,|1.7 pp. 54-55 #1-37 odd (skip 11,19,21, 29, 31) 50-53 |

| |Word Problems | |

| |(p. 55 #21; if time go over graph for #s 33-37) | |

|3 |More of Days 1 and 2 |WORKSHEETS in Packet |

|4 |Review (10-15 min.) |TBD |

| |QUIZ | |

|5 |Intro to 5 “Parent Functions” (Constant, Linear, Quadratic, Cubic, |1.9 pp.70-73 #1-7, 11, 12, 17-19 (use the table feature on |

| |Square Root) and their transformations (Using Graphing Calculator) |calc to help) |

|6 |Compound Inequalities |2.8 pp.154-156 # 1-4, 14, 15, 28-36 (HW in PACKET) |

|7 |Absolute Value Equations |2.8 pp.154-156 #5-7, 16-19, 38, 49 |

|8 |Absolute Value Inequalities |2.8 pp.154-156 #8-13, 36, 39, 41, 42, 55-58 |

|9 |Absolute Value Functions – Graphs, Translations, Reflections |2.9 pp.161-163 # 2-6, 19-24, 27-29, 33, 36 |

|10 |Review | pp. 78 #36-46, 53-54, p. 169 #47-56, 58 |

| | |or a worksheet |

|11 |More Review |Worksheet |

| |And Word Problems | |

|12 |TEST |See page 31 of packet |

Reminders:

Bring your calculator every day.

Missed Tests/Quizzes:

avoid 20% reduction; don’t forget. Manage your school work please.

Mini Quizzes are always open-note.

Work hard but try not to stress. Life REALLY is too short.

A _____________________is a set of pairs of input and output values. You can write them as ordered pairs.

The ___________________ of a relation is the set of all inputs, or x-coordinates of the ordered pairs.

The ____________________ of a relation is the set of all outputs, or y-coordinates of the ordered pairs.

A _______________________ is a relation in which each element of the domain is paired with exactly one element in the range.

Look for: The same x-value, but different y-values! This means it is not a function!

Are the following relations function? State why or why not! Then state the domain and range!

a) [pic] b) [pic]

Function: _________ Function: _________

Domain: __________________ Domain: __________________

Range: ___________________ Range: ___________________

Mapping Diagram: Identify the domain and range. Then tell whether the relation is a function.

Input Output Input Output

-3 3 -3 3

1 -2 1 1

4 1 3

4 4 -2

Function: _________ Function: _________

Domain: __________________ Domain: __________________

Range: ___________________ Range: ___________________

Vertical Line test: A relation is a function if and only if no vertical line intersects the graph of the relation at more than one point. If a vertical line passes through two or more points on the graph, then the relations is not a function.

Using the Vertical Line Test, determine whether each relation is a function. Then state the domain & range.

[pic]

Function: _________ Function: _________ Function: _________

Domain: __________________ Domain: __________________ Domain: __________________

Range: ___________________ Range: ___________________ Range: ___________________

Function: _________ Function: _________

Domain: __________________ Domain: __________________

Range: ___________________ Range: ___________________

For a graph to be a function, all vertical lines must touch in only _____ spot (or not touch at all)

For the domain, scan your eyes from __________ to ___________.

For the range, scan your eyes from the ___________________ to the ___________.

|Earnings Per Hour |

|Name |Bob |Dave |Jane |Sam |

|Pay |$9 |$11 |$5 |$15 |

|Test Scores |

|Name |Jim |Greg |Jorge |Terrell |

|Score |65 |91 |94 |88 |

Function: _________ Function: _________

Domain: __________________ Domain: __________________

Range: ___________________ Range: ___________________

Closure

Why is [pic] a function, but [pic]is not?

Function Notation:

[pic] can be written in a “fancy notation” ( [pic].

[pic] is read as _________________________ and does NOT mean f times x.

|“Normal Way” |Function Way |

|[pic] |[pic] |

|Simplify [pic] when [pic] |[pic]; find [pic] |

Given [pic] and [pic], find the following:

a) [pic] b) [pic] c) [pic]

d) [pic] e) [pic] f) * [pic]

Find [pic]. Find [pic].

Graphing functions: Do this the same why we learned to graph lines, but just replace the [pic](or whatever letter it is) with ______!

Example: [pic] Example 2:[pic] Example 3: [pic]

Word Problems: FUN FUN FUN!

[pic]

[pic]

[pic]

Directions: Explain a possible domain and range for each situation

[pic]

[pic]

[pic]

Directions: Graph each function below

[pic]

[pic]

Function: _________ Function: _________

Domain: __________________ Domain: __________________

Range: ___________________ Range: ___________________

[pic]

Directions: For each graph below, determine it is a function (what’s the vertical line test?). Then write the domain and range. Finally, for each graph, find the output for the corresponding input. Remember, there could be more than one!

Function: _______________ Function: _______________ Function: _______________

Domain: _______________ Domain: _______________ Domain: _______________

Range: _________________ Range: _________________ Range: _________________

[pic] ________________ [pic] ________________ [pic] ________________

Function: _______________ Function: _______________ Function: _______________

Domain: _______________ Domain: _______________ Domain: _______________

Range: _________________ Range: _________________ Range: _________________

[pic] ________________ [pic] ________________ [pic] ________________

Graph the function [pic] on your calculator. Sketch the graph on the axis, and fill in the table of values.

|x |y |

|-3 | |

|-2 | |

|-1 | |

|0 | |

|1 | |

|2 | |

|3 | |

|x |y |

|-3 | |

|-2 | |

|-1 | |

|0 | |

|1 | |

|2 | |

|3 | |

Look at the function, [pic]. Graph this function on your calculator, sketch the graph on the axis, and fill in the table of values.

How is this function different from the first one?

What do you think the function [pic] looks like?

Check your guess on your calculator.

Use your calculator to graph each of the functions below, sketch the graph on the axis, and describe how each one is different than [pic].

1. [pic]

This is like [pic], but…

___________________________.

2. [pic]

This is like [pic], but…

___________________________.

3. [pic]

This is like [pic], but…

___________________________.

4. [pic]

This is like [pic], but…

___________________________.

5. [pic]

This is like [pic], but…

___________________________.

6. [pic]

This is like [pic], but…

___________________________

The basic function that we were working with is known as a ____________________ function. The “shifts” (________________________) that we saw will occur in other “parents” as well.

|Linear |Square Root |Cubic |Quadratic |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

|[pic] |[pic] |[pic] |[pic] |

| |

|EXAMPLES Shifts |

| |

|[pic] |[pic] |[pic] |[pic] | |

|[pic] |[pic] |[pic] |[pic] | |

|“Impossible” |[pic] |[pic] |[pic] | |

|“Impossible” |[pic] |[pic] |[pic] | |

Directions: Name the parent function, and then describe the translation that will occur.

1) [pic]

2) [pic]

3) [pic]

4) [pic]

5) [pic]

6) [pic]

Directions: Now, word backwards. I’ll give you the translation, you write the function.

7) [pic] Translate 5 units left and 1 units down

8) [pic] Translate 1 unit down

9) [pic] Translate 2 units left and 1 unit up

10) [pic] Translate 3 units down

11) [pic] Translate 6 units right

Wrap Up:

a) What is a parent function?

b) How do translations occur? Can we generalize those translations?

c) Why is math so fun?

Warmup: Solve each inequality. Do not forget the rule that we learned in the previous chapter.

a) [pic] b) [pic] c) [pic] d) [pic]

Today we are going to discuss _______________________ inequalities. Basically this is just the combination of 2 inequalities onto one graph. There are ______ different cases to consider.

OR ( Shade both inequalities separately, but on the same graph.

AND ( Shade only the _________________ of the two graphs!

Let’s combine warmup problems a) and b) with OR, and c) and d) with AND.

Practice:

[pic]

[pic]

Fancy: Combining an AND statement (

Now, work _____________________. I give you the graph, you come up with the inequality.

8) 9)

10) 11)

Closure:

1) Describe the difference between an “AND” and “OR” compound inequality

2) What is the one key you need to remember when solving inequalities?

Extension: HW Start! The problems from the book are below.

The absolute value of a number is always ___________________. The technical definition is the __________________ from ______.

Therefore, [pic] = _____, and when [pic]that means that [pic]______ or _______!

Because numbers inside the absolute value can be _______________ or negative, we must account for two separate cases.

Example 1: [pic] Example 2: [pic]

Example 3: [pic] Example 4: [pic]

Example 5: Work backwards ( Answer is [pic]

Warmup: Solve the two compound inequalities below and then graph!

a) [pic] or [pic] b) [pic]

When solving absolute value ________________________, we create compound inequalities like the ones we saw in the warmup. There are two distinct cases that cause the two cases: ____________ & ________.

CASE #1: [pic] (

CASE #2: [pic] (

Note: “or equal to” is treated the same!

a) [pic] b) [pic]

[pic]

[pic]

[pic]

In order to graph absolute value functions on your calculator, when you’re in the functions list, push the MATH key, then the right arrow to get to the NUMber submenu. abs( is the first function on the list.

|x |y |

|-3 | |

|-2 | |

|-1 | |

|0 | |

|1 | |

|2 | |

|3 | |

Graph the function [pic] on your calculator. Sketch the graph on the axis, and fill in the table of values.

|x |y |

|-3 | |

|-2 | |

|-1 | |

|0 | |

|1 | |

|2 | |

|3 | |

Look at the function, [pic]. Graph this function on your calculator, sketch the graph on the axis, and fill in the table of values.

How is this function different from the first one?

What do you think the function [pic] looks like?

Check your guess on your calculator.

Use your calculator to graph each of the functions below, sketch the graph on the axis, and describe how each one is different than[pic].

1. [pic]

This is like [pic], but moved…

___________________________.

2. [pic]

This is like [pic], but moved…

___________________________.

3. [pic]

This is like [pic], but moved…

___________________________.

4. [pic]

This is like [pic], but moved…

___________________________.

5. [pic]

This is like [pic], but moved…

___________________________.

6. [pic]

This is like [pic], but moved…

___________________________.

In general, we can say that the function [pic] is like the [pic], but moved ________________________________________.

Another way we can say this is that it is the same shape as [pic], but with a new vertex at _______.

There are other translations that can happen to a parent function:

1. [pic] 3. [pic]

This is like [pic], but… This is like [pic], but…

___________________________. ___________________________.

2. [pic] 4. [pic]

This is like [pic], but… This is like [pic], but…

___________________________. ___________________________.

Conclusion:

Tell whether the graph is the graph of a function. Then state the Domain and Range for each in interval notation.

1. 2.

Function? ___________ Function? ___________

Domain: ____________ Domain: ____________

Range: _____________ Range: _____________

Show all your work, and evaluate each of the following for the functions:

[pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

7. Consider the equation [pic].

a) Describe how you would use the graph of [pic] to graph the function [pic]. In other words, how would you move the original graph to accurately place the new one?

b) What are the coordinates of vertex of g(x)?

8. What is a parent function? Use examples in your answer.

Solve, and graph your solution on a number line.

9. [pic]

10. [pic]

11. [pic]

Solve each equation.

12. [pic]

13. [pic]

14. [pic]

Solve each inequality, and graph your solution on a number line.

15. [pic]

16. [pic]

17. [pic]

Write the equation of each absolute value function.

18. 19.

[pic]__________________ [pic]__________________

Answers!

1. yes, (-2, 4], (-3, 3]

2. no, [1, infinity), (-infinity, infinity)

3. -13

4. 6

5. 56

6. -1

7. a) left 7, down 2

b) (-7, -2)

9. (4, 7]

Directions: For each function below, please name the parent function and the translation that is caused.

1) [pic]

2) [pic]

3) [pic]

4) [pic]

5) [pic]

Directions: Now, word backwards. I’ll give you the translation, you write the function.

6) [pic] Translate 2 units left and 5 units down

7) [pic] Translate 1 unit up

8) [pic] Translate 9 units right and 1 unit down

9) [pic] Translate 7 units up

10) [pic] Translate 6 units right

11) Directions: Use the graph of each function to evaluate

[pic][pic] [pic]

a) [pic] [pic]

b) [pic] [pic]

c) [pic] [pic]

d) [pic] [pic]

e) [pic] [pic]

12) Directions: Write the domain and range of each graph in interval notation.

a) b) c)

Complete these problems from the textbook. Please be sure to show your work and write the answer in the space provided.

|Pg. 81, #1 |Pg. 84, #1 |

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|Answer: |Answer: |

|Pg. 84, #2 |Pg. 171, #3 |

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|Answer: |Answer: |

|Pg. 171, #6 |Pg. 174, #1 |

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|Answer: |Answer: |

|Pg. 174, #7 |Pg. 174, #11 |

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|Answer: |Answer: |

-----------------------

U2 D1: Domain, Range, Relations vs. Functions & V. Line Test

Date _________ Period_________

U2 D2: Function Notation, Indep./Dep. Variables & Graphing

a)

b)

c)

e)

d)

U2 D3: Practice from Day’s 1 & 2

a) [pic]

a) [pic] b) [pic]

U2 D5: Intro to Parent Functions

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

U2 D7: Absolute Value Equations

U2 D6: Compound Inequalities

U2 D8: Absolute Value Inequalities

Date _________ Period_________

U2 D9: Absolute Value Functions – Graphs, Translations, Refl.

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

U2 D10: Unit 2 Review

[pic]

[pic]

[pic]

[pic]

10. (-infinity, -4] or [5, infinity)

11. (-5, infinity)

12. -7, 15

13. -3/2, -1

14. -2, 6

15. (-infinity, -1) or (7, infinity)

16. [1/2, 5/2]

17. (-infinity, -4/5] or [6/5, infinity)

U2 D11: Unit 2 Review #2 with More Translations

U2 D12: Unit 2 Homework After the Test

Date _________ Period_________

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