Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph...
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Transcript of Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph...
![Page 1: Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.](https://reader033.fdocuments.us/reader033/viewer/2022051215/5697bfbd1a28abf838ca220d/html5/thumbnails/1.jpg)
Notes Over 2.3The Graph of a FunctionThe Graph of a FunctionFinding the Domain and Range of a Function. 1. Use the graph of the function f to find the domain of f.
,2 52. Find the value of f(-2),
and f(2).
2f 4
3. Find the range of the graph.
,4 4
2f 4
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Notes Over 2.3Zeros of a FunctionZeros of a FunctionFinding Zeros of a Function. Find the zeros of each function.
055 .4 23 xxx
x 2x 1
5x 012 x
0 5 2x 1
0 1x 1x 5x5x 1x 1x
![Page 3: Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.](https://reader033.fdocuments.us/reader033/viewer/2022051215/5697bfbd1a28abf838ca220d/html5/thumbnails/3.jpg)
Notes Over 2.3Zeros of a FunctionZeros of a FunctionFinding Zeros of a Function. Find the zeros of each function.
0 15 .5 2 x215 x 0
2 2
2x15
15x
![Page 4: Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.](https://reader033.fdocuments.us/reader033/viewer/2022051215/5697bfbd1a28abf838ca220d/html5/thumbnails/4.jpg)
Notes Over 2.3Zeros of a FunctionZeros of a FunctionFinding Zeros of a Function. Find the zeros of each function.
04
417 .6
2
x
x
0471 x417 x
4
17x
![Page 5: Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.](https://reader033.fdocuments.us/reader033/viewer/2022051215/5697bfbd1a28abf838ca220d/html5/thumbnails/5.jpg)
Notes Over 2.3Increasing and Decreasing FunctionsIncreasing and Decreasing FunctionsDescribe the increasing and decreasing behavior.
The function is decreasing over
the entire real line.
.7
![Page 6: Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.](https://reader033.fdocuments.us/reader033/viewer/2022051215/5697bfbd1a28abf838ca220d/html5/thumbnails/6.jpg)
Notes Over 2.3Increasing and Decreasing FunctionsIncreasing and Decreasing FunctionsDescribe the increasing and decreasing behavior.
The function is decreasing on the interval , 1increasing on the interval ,1 0decreasing on the interval ,0 1increasing on the interval ,1
.8
![Page 7: Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.](https://reader033.fdocuments.us/reader033/viewer/2022051215/5697bfbd1a28abf838ca220d/html5/thumbnails/7.jpg)
Notes Over 2.3Increasing and Decreasing FunctionsIncreasing and Decreasing FunctionsDescribe the increasing and decreasing behavior.
The function is increasing on the interval ,4 1constant on the interval ,1 2
decreasing on the interval ,2 5
.9
![Page 8: Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.](https://reader033.fdocuments.us/reader033/viewer/2022051215/5697bfbd1a28abf838ca220d/html5/thumbnails/8.jpg)
Notes Over 2.3Increasing and Decreasing FunctionsIncreasing and Decreasing FunctionsDetermining Relative Maximum or Minimum.
Relative Maximum
Relative Minimum
![Page 9: Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.](https://reader033.fdocuments.us/reader033/viewer/2022051215/5697bfbd1a28abf838ca220d/html5/thumbnails/9.jpg)
Notes Over 2.3Increasing and Decreasing FunctionsIncreasing and Decreasing FunctionsDetermining Relative Maximum or Minimum. 10.Use a graphing calculator to find the relative
maximum of the function:
11102 2 xxy
5.1 ,5.2
![Page 10: Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.](https://reader033.fdocuments.us/reader033/viewer/2022051215/5697bfbd1a28abf838ca220d/html5/thumbnails/10.jpg)
Notes Over 2.3Linear FunctionsLinear Functions11. Write the linear function f for which 14 f
5
1
2
31 m
10 64
and 36 f
y1y
11 xxmyy
x5
1
1 45
1
5
4 x
5
1
5
9
![Page 11: Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.](https://reader033.fdocuments.us/reader033/viewer/2022051215/5697bfbd1a28abf838ca220d/html5/thumbnails/11.jpg)
Notes Over 2.3Graphing a Piecewise FunctionGraphing a Piecewise Function
Graph the function.
2 if ,92
2 if ,42
1 .12
xx
xxxf
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Notes Over 2.3Even and Odd FunctionsEven and Odd FunctionsDetermine if the function is even, odd, or neither.
24 2 .13 xxxf even isfunction then the, If xfxf odd isfunction then the, If xfxf
24 2 xf x x
24 2xxxf
Even function
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Notes Over 2.3Even and Odd FunctionsEven and Odd FunctionsDetermine if the function is even, odd, or neither.
xxxf 45 .14 3 even isfunction then the, If xfxf odd isfunction then the, If xfxf
4 5 3 xf x x
xxxf 45 3 Odd function
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Notes Over 2.3