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## PowerPoint Slideshow about 'Algebra II Honors—Day 10' - mickey

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Procedures

- Pick up the following from the table:
- Handout, whiteboard, marker, eraser
- Get into groups of three or four students.

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

Essential Questions

- How do the values of a, b, c, and d in the function affect the graph of ?

The absolute value function is a function of the form

It has a two-part definition as follows:

for

and for

Exploring the Absolute Value FunctionThe Graph

For x<0, the graph is the same as the line y=-x (intercept of 0 and slope of NEGATIVE 1)

For x≥0, the graph is the same as the line y=x (intercept of 0 and slope of POSITIVE 1)

y=|x|

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.

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.

The effect of “a” (the number outside the function—multiplies the entire function)

The parent function

- 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

The effects of “b” and “c” (the numbers inside the function—“b” multiplies the x only)

The parent function

- 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

The effects of “b” and “c” (the numbers inside the function—“b” multiplies the x only)

The parent function

- 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”)

The effects of “d” (the number added outside the function)

The parent function

- d=8
- New function is shifted UP 8 units (“d”)

- d=-6
- New function is shifted DOWN 6 units (“d”)

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.

Homework

- Absolute Value Graphs
- Do without a calculator based on what you learned.

Problems 1, 2, 4, 7, 8, 9, 10, 12

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