Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations...
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Transcript of Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations...
![Page 1: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/1.jpg)
Daily Check
Graph the following equations.
1. 3 2
2. 2
y x
y x
![Page 2: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/2.jpg)
Math II
UNIT QUESTION: How are absolute value equations similar to piecewise functions?Standard: MM2A1
Today’s Question:How are absolute value equations similar to piecewise functions?Standard: MM2A1.a,b
![Page 3: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/3.jpg)
Absolute Value as Piecewise Functions
Section 2.5
![Page 4: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/4.jpg)
Piecewise Functions
Piecewise functions are functions that can be represented by more than one equation, with each equation corresponding to a different part of the domain.
Piecewise functions do not always have to be line segments. The “pieces” could be pieces of any type of graph.
This type of function is often used to represent real-life problems like ticket prices.
![Page 5: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/5.jpg)
Example
f (x) =
x + 1, if x < 1
2, if 1 ≤ x ≤ 3
(x-3)2 + 2, if x > 3
![Page 6: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/6.jpg)
Absolute Value as Piecewise
We usually write an absolute value function as f (x)= x , but since absolute value is a measure of distance and distance is always positive, it also can be written as follows:
f (x) = -x, if x < 0
x, if x ≥ 0
![Page 7: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/7.jpg)
Writing Abs. Value as Piecewise
For I x – h I ≥ 0, simplify the equation given by distributing and combining like terms.
For I x – h I < 0, substitute –(x – h) in place of I x - h I. Then, simplify.
![Page 8: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/8.jpg)
Example
Write y = 2 Ix – 4I – 10 as a piecewise function.
For (x-4) ≥ 0
2(x – 4) – 10 = 2x – 8 – 10 = 2x – 18 (when x ≥ 4)
For (x-4) < 0
2[-(x-4)] – 10 = 2(-x + 4) – 10 = -2x + 8 – 10
= -2x – 2 (when x < 4))
![Page 9: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/9.jpg)
Graphs of Both
y=2x-18y=-2x-2
![Page 10: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/10.jpg)
EOCT Practice
A
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EOCT Practice
C
![Page 12: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/12.jpg)
Writing Abs. Value as Piecewise
Using a graph
![Page 13: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/13.jpg)
Writing Abs. Value as Piecewise
Try this one...
![Page 14: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/14.jpg)
Practice
Worksheet
![Page 15: Daily Check Graph the following equations.. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649ef05503460f94c00066/html5/thumbnails/15.jpg)
Homework
Worksheet