Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout,...
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Transcript of Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout,...
![Page 1: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/1.jpg)
Algebra II Honors—Day 10
![Page 2: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/2.jpg)
Procedures
• Pick up the following from the table:– Handout, whiteboard, marker, eraser
• Get into groups of three or four students.
![Page 3: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/3.jpg)
Goals for Today
• Reminder—First Graded Homework Assignment (checked for accuracy)—tomorrow—Tuesday, Sept. 10
• Quotable Puzzle due today• No homework check today• Essential Questions
– New Material/Group Investigations• Homework
![Page 4: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/4.jpg)
Essential Questions
• How do the values of a, b, c, and d in the function affect the graph of ?xxf )(
dcbxaxf )(
![Page 5: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/5.jpg)
Exploring the Absolute Value Function
• The absolute value function is a function of the form
• It has a two-part definition as follows: for
and for
xy
xy 0x
xy 0x
![Page 6: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/6.jpg)
The Graph
For x≥0, the graph is the same as the line y=x (intercept of 0 and slope of POSITIVE 1)
For x<0, the graph is the same as the line y=-x (intercept of 0 and slope of NEGATIVE 1)
y=|x|
![Page 7: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/7.jpg)
Explanations
• f(x)=a|bx+c|+d
The letters a, b, c, and d represent shifts or changes to the basic “parent” graph of f(x)=|x|. Each of these plays a different role in the movement of the graph. You will explore each.
![Page 8: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/8.jpg)
Assignment• Within each group divide up the work in each section
on the handout and then compare answers for all the parts. Use the whiteboards first until all graphs are finished.
• Draw the basic graph: f(x)=|x|. This is called the “parent graph” or the “parent function.”
• Make a table of points for the other equations and graph each one on the same coordinate plane. For each graph, use the domain {-3, -1, 0, 1, 3} and find the y-values. Then draw the graph.
![Page 9: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/9.jpg)
The effect of “a” (the number outside the function—multiplies the entire function)
xxf 3)(
The parent function
xxf2
1)(
xxf )(
New function “grows” faster• called a “vertical stretch”• slope is steeper—
multiplied by “a”
New function “grows” slower• called a “vertical shrink”• slope is less steep—
multiplied by “a”• the negative flips it upside
down as well
![Page 10: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/10.jpg)
The effects of “b” and “c” (the numbers inside the function—“b” multiplies the x only)
3)( xxf
The parent function
5)( xxf
xxf )(
b=1 and c=3• New function is shifted
LEFT 3 units (“-c”) and slope is still the same as parent
b=1 and c=-5• New function is shifted
RIGHT 5 units (“-c”) and slope is still the same as parent
![Page 11: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/11.jpg)
The effects of “b” and “c” (the numbers inside the function—“b” multiplies the x only)
36)( xxf
The parent function
93)( xxf
xxf )(
b=6 and c=3• New function is shifted
LEFT 1/2 unit (“-c/b”) and slope is multiplied by 6 (“b”)
b=3 and c=-9• New function is shifted
RIGHT 3 units (“-c/b”)and slope is multiplied by 3 (“b”)
![Page 12: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/12.jpg)
The effects of “d” (the number added outside the function)
8)( xxf
The parent function
6)( xxf
xxf )(
d=8• New
function is shifted UP 8 units (“d”)
d=-6• New
function is shifted DOWN 6 units (“d”)
![Page 13: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/13.jpg)
In your notes
• Make sure you can summarize the effects of each of the numbers a, b, c, and d in the equation . These numbers will be used throughout this course for other functions.
• Understand that each of these numbers either “shifts” or “stretches” the parent function.
dcbxaxf )(
![Page 14: Algebra II Honors—Day 10. Procedures Pick up the following from the table: – Handout, whiteboard, marker, eraser Get into groups of three or four students.](https://reader036.fdocuments.us/reader036/viewer/2022082711/56649f285503460f94c40041/html5/thumbnails/14.jpg)
Homework
• Absolute Value Graphs– Do without a calculator based on what you
learned.Problems 1, 2, 4, 7, 8, 9, 10, 12