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.

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 ?

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

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|

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