lesson 1-3 new functions from old functions part 1 - part 1 ...
TRANSCRIPT
![Page 1: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/1.jpg)
Lesson 1-3Lesson 1-3New Functions
from Old Functions - Part 1Part 1
https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Qu308QRANh_v4UHWiw
![Page 2: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/2.jpg)
At this point in time it is important to know and remember certain
parent functions and their graphs.
![Page 3: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/3.jpg)
Now, by recognizing a parent functions graph and then
applying certain transformations, we can see how various
other graphs can be obtained.
![Page 4: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/4.jpg)
We are going to want to sketch these other graphs by hand and also come up with their
equations.
![Page 5: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/5.jpg)
Let’s first consider translations. Simply by adding or subtracting a
constant c to a formula of a function can cause a slide up,
down, right, or left, of a parent functions graph.
![Page 6: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/6.jpg)
Vertical and Horizontal shifts:
![Page 7: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/7.jpg)
Vertical and Horizontal shifts: Suppose c > 0, to obtain
![Page 8: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/8.jpg)
Vertical and Horizontal shifts: Suppose c > 0, to obtain y = f(x) + c shift the graph of y = f(x) a distance of c units upward y = f(x) – c shift the graph of y = f(x) a distance of c units downward y = f(x – c) shift the graph of y = f(x) a distance of c units to the right y = f(x + c) shift the graph of y = f(x) a distance of c units to the left
![Page 9: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/9.jpg)
Vertical and Horizontal shifts: Suppose c > 0, to obtain y = f(x) + c shift the graph of y = f(x) a distance of c units upward y = f(x) – c shift the graph of y = f(x) a distance of c units downward y = f(x – c) shift the graph of y = f(x) a distance of c units to the right y = f(x + c) shift the graph of y = f(x) a distance of c units to the left
![Page 10: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/10.jpg)
Vertical and Horizontal shifts: Suppose c > 0, to obtain y = f(x) + c shift the graph of y = f(x) a distance of c units upward y = f(x) – c shift the graph of y = f(x) a distance of c units downward y = f(x – c) shift the graph of y = f(x) a distance of c units to the right y = f(x + c) shift the graph of y = f(x) a distance of c units to the left
Catchy little phrase: Add to y means go “high”, add to x means go “west”.
![Page 11: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/11.jpg)
Example:
![Page 12: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/12.jpg)
Example:
![Page 13: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/13.jpg)
Example:
![Page 14: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/14.jpg)
Example:
![Page 15: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/15.jpg)
Example:
![Page 16: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/16.jpg)
Example:
![Page 17: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/17.jpg)
Example:
![Page 18: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/18.jpg)
When multiplying or dividing by a constant, this can produce various kinds of stretching, shrinking, or
reflections of the graph of a function.
![Page 19: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/19.jpg)
Vertical and Horizontal Stretching and Reflecting Suppose c > 1, to obtain
![Page 20: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/20.jpg)
Vertical and Horizontal Stretching and Reflecting Suppose c > 1, to obtain
y = cf(x), stretch the graph of y = f(x) vertically by a factor of c y = (1/c)f(x), compress the graph of y = f(x) vertically by a factor of c y = f(cx), compress the graph of y = f(x) horizontally by a factor of c y = f(x/c), stretch the graph of y = f(x) horizontally by a factor of c y = - f(x), reflect the graph of y = f(x) about the x-axis y = f(-x), reflect the graph of y = f(x) about the y-axis
![Page 21: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/21.jpg)
Example:
![Page 22: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/22.jpg)
Example:
The most common mistake made is to do the transformations in the wrong order!
![Page 23: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/23.jpg)
Example:
The most common mistake made is to do the transformations in the wrong order!
(Hint: Follow rules for order of operations.) (pemdas)
![Page 24: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/24.jpg)
Example:
![Page 25: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/25.jpg)
Example:
![Page 26: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/26.jpg)
Example:
![Page 27: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/27.jpg)
Example:
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Compare the results of y = cf(x) and y = f(cx).
![Page 29: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/29.jpg)
![Page 30: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/30.jpg)
![Page 31: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/31.jpg)
Now lets take a look at what absolute value | |
surrounding a function does to a graph.
![Page 32: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/32.jpg)
When you take the absolute value of a function f(x), the graph of|f(x)| will be the graph of f(x)
except that the part of the graph of f(x) below the x axis will be reflected above the x-axis!
![Page 33: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/33.jpg)
Take the graph of y = sin x.
![Page 34: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/34.jpg)
Now, sketch the graph of y = | sin x |.
![Page 35: Lesson 1-3 New Functions from Old Functions Part 1 - Part 1 tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q](https://reader035.vdocument.in/reader035/viewer/2022062421/56649cbb5503460f94983b10/html5/thumbnails/35.jpg)
Assignment:
Pgs. 43-44#3, 5, 9-23 odd