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 / ASSIGNMENT1 / Domain, Range, Relations vs. Functions, Vertical Line Test(p. 48 #21, 31-37 if time) / 1.6 pp. 47-48 #1-29 ODD, 31-33 (skip 5,11,21) 44, 46
2 / Function notation, independent/dependentVariables, Graphing Functions, Word Problems
(p. 55 #21; if time go over graph for #s 33-37) / 1.7 pp. 54-55 #1-37 odd (skip 11,19,21, 29, 31) 50-53
3 / More of Days 1 and 2 / WORKSHEETS in Packet
4 / Review (10-15 min.)
QUIZ / TBD
5 / Intro to 5 “Parent Functions” (Constant, Linear, Quadratic, Cubic, Square Root) and their transformations (Using Graphing Calculator) / 1.9 pp.70-73 #1-7, 11, 12, 17-19 (use the table feature on 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
And Word Problems / Worksheet
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) b)
Function: ______Function: ______
Domain: ______Domain: ______
Range: ______Range: ______
Mapping Diagram: Identify the domain and range. Then tell whether the relation is a function.
InputOutputInputOutput
-33-33
1-211
413
44-2
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.
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 HourName / 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 a function, but is not?
Function Notation:
can be written in a “fancy notation” .
is read as ______and does NOT mean f times x.
“Normal Way” / Function WaySimplify when / ; find
Given and , find the following:
a) b) c)
d) e) f) *
Find . Find .
Graphing functions: Do this the same why we learned to graph lines, but just replace the (or whatever letter it is) with ______!
Example: Example 2: Example 3:
Word Problems: FUN FUN FUN!
Directions: Explain a possible domain and range for each situation
Directions: Graph each function below
Function: ______Function: ______
Domain: ______Domain: ______
Range: ______Range: ______
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: ______
______ ______ ______
Function: ______Function: ______Function: ______
Domain: ______Domain: ______Domain: ______
Range: ______Range: ______Range: ______
______ ______ ______
Graph the function 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, . 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 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 .
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1.
This is like , but…
______.
2.
This is like , but…
______.
3.
This is like , but…
______.
4.
This is like , but…
______.
5.
This is like , but…
______.
6.
This is like , but…
______
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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 / QuadraticEXAMPLES Shifts
“Impossible” / / /
“Impossible” / / /
Directions: Name the parent function, and then describe the translation that will occur.
1)
2)
3)
4)
5)
6)
Directions: Now, word backwards. I’ll give you the translation, you write the function.
7) Translate 5 units left and 1 units down
8) Translate 1 unit down
9) Translate 2 units left and 1 unit up
10) Translate 3 units down
11) 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) b) c) d)
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:
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, = _____, and when that means that ______or ______!
Because numbers inside the absolute value can be ______or negative, we must account for two separate cases.
Example 1: Example 2:
Example 3: Example 4:
Example 5: Work backwards Answer is
Warmup: Solve the two compound inequalities below and then graph!
a) or b)
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:
CASE #2:
Note: “or equal to” is treated the same!
a) b)
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 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, . 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 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.
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1.
This is like , but moved…
______.
2.
This is like , but moved…
______.
3.
This is like , but moved…
______.
4.
This is like , but moved…
______.
5.
This is like , but moved…
______.
6.
This is like , but moved…
______.
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In general, we can say that the function is like the , but moved ______.
Another way we can say this is that it is the same shape as , but with a new vertex at ______.
There are other translations that can happen to a parent function:
1.3.
This is like , but…This is like , but…
______.______.
2.4.
This is like , but…This is like , 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:
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3.
4.
5.
6.
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7. Consider the equation .
a) Describe how you would use the graph of to graph the function . 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.
10.
11.
Solve each equation.
12.
13.
14.
Solve each inequality, and graph your solution on a number line.
15.
16.
17.
Write the equation of each absolute value function.
18. 19.
____________
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)
2)
3)
4)
5)
Directions: Now, word backwards. I’ll give you the translation, you write the function.
6) Translate 2 units left and 5 units down
7) Translate 1 unit up
8) Translate 9 units right and 1 unit down
9) Translate 7 units up
10) Translate 6 units right
11) Directions: Use the graph of each function to evaluate
a)
b)
c)
d)
e)
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, #1Answer: / Pg. 84, #1
Answer:
Pg. 84, #2
Answer: / Pg. 171, #3
Answer:
Pg. 171, #6
Answer: / Pg. 174, #1
Answer:
Pg. 174, #7
Answer: / Pg. 174, #11
Answer:
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