1.7 - functions
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1.7 - Functions. 1.7 - Functions. A function is a relation in which each element of the domain is paired with exactly one element of the range. 1.7 - Functions. A function is a relation in which each element of the domain is paired with exactly one element of the range. 1.7 - Functions. - PowerPoint PPT PresentationTRANSCRIPT
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1.7 - Functions
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1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
![Page 3: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/3.jpg)
1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
![Page 4: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/4.jpg)
1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
![Page 5: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/5.jpg)
1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
![Page 6: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/6.jpg)
1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
There cannot be an x-value repeated!
![Page 7: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/7.jpg)
1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
There cannot be an x-value repeated!
![Page 8: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/8.jpg)
1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
There cannot be an x-value repeated!
Ex.1 Determine if each is a function.
![Page 9: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/9.jpg)
1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
There cannot be an x-value repeated!
Ex.1 Determine if each is a function.
a. X Y
-6
-4 9
-1 -6
1 1
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1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
There cannot be an x-value repeated!
Ex.1 Determine if each is a function.
a. X Y
-6
-4 9 Y
-1 -6 E
1 1 S
![Page 11: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/11.jpg)
1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
There cannot be an x-value repeated!
Ex.1 Determine if each is a function.
a. X Y b.
-6
-4 9 Y
-1 -6 E
1 1 S
x y
-3 6
2 5
3 1
2 4
![Page 12: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/12.jpg)
1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
There cannot be an x-value repeated!
Ex.1 Determine if each is a function.
a. X Y b.
-6
-4 9 Y
-1 -6 E
1 1 S
x y
-3 6
2 5
3 1
2 4
![Page 13: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/13.jpg)
1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
There cannot be an x-value repeated!
Ex.1 Determine if each is a function.
a. X Y b.
-6
-4 9 Y
-1 -6 E
1 1 S
x y
-3 6
2 5
3 1
2 4
![Page 14: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/14.jpg)
1.7 - Functions• A function is a relation in which each
element of the domain is paired with exactly one element of the range.
There cannot be an x-value repeated!
Ex.1 Determine if each is a function.
a. X Y b.
-6 NOT A
-4 9 Y FUNC.
-1 -6 E
1 1 S
x y
-3 6
2 5
3 1
2 4
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Ex. 2 If f(x) = x2 – 5, find the following:
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Ex. 2 If f(x) = x2 – 5, find the following:
a. f(-9)
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Ex. 2 If f(x) = x2 – 5, find the following:
a. f(-9)
f(x) = x2 – 5
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Ex. 2 If f(x) = x2 – 5, find the following:
a. f(-9)
f(x) = x2 – 5
f(-9)
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Ex. 2 If f(x) = x2 – 5, find the following:
a. f(-9)
f(x) = x2 – 5
f(-9)
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a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2
Ex. 2 If f(x) = x2 – 5, find the following:
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a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
Ex. 2 If f(x) = x2 – 5, find the following:
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a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
Ex. 2 If f(x) = x2 – 5, find the following:
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a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
Ex. 2 If f(x) = x2 – 5, find the following:
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a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
Ex. 2 If f(x) = x2 – 5, find the following:
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a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 26: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/26.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) =
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 27: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/27.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 28: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/28.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
= 62
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 29: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/29.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
= 62·z2
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 30: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/30.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
= 62·z2 – 5
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 31: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/31.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
= 62·z2 – 5
f(6z) = 36z2 – 5
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 32: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/32.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
= 62·z2 – 5
f(6z) = 36z2 – 5
c. f(4) + 2
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 33: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/33.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
= 62·z2 – 5
f(6z) = 36z2 – 5
c. f(4) + 2 f(4) + 2 =
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 34: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/34.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
= 62·z2 – 5
f(6z) = 36z2 – 5
c. f(4) + 2 f(4) + 2 = [(4)2 – 5]
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 35: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/35.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
= 62·z2 – 5
f(6z) = 36z2 – 5
c. f(4) + 2 f(4) + 2 =[(4)2 – 5]
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 36: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/36.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
= 62·z2 – 5
f(6z) = 36z2 – 5
c. f(4) + 2 f(4) + 2 =[(4)2 – 5] + 2
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 37: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/37.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
= 62·z2 – 5
f(6z) = 36z2 – 5
c. f(4) + 2 f(4) + 2 = [(4)2 – 5] + 2
= [16 – 5] + 2
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 38: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/38.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
= 62·z2 – 5
f(6z) = 36z2 – 5
c. f(4) + 2 f(4) + 2 = [(4)2 – 5] + 2
= [16 – 5] + 2 = 11 + 2
Ex. 2 If f(x) = x2 – 5, find the following:
![Page 39: 1.7 - Functions](https://reader036.vdocuments.net/reader036/viewer/2022081421/56814356550346895dafd2ac/html5/thumbnails/39.jpg)
a. f(-9)
f(x) = x2 – 5 f(-9) = (-9)2 – 5
= 81 – 5
f(-9) = 76
b. f(6z)
f(x) = x2 – 5
f(6z) = (6z)2 – 5
= 62·z2 – 5
f(6z) = 36z2 – 5
c. f(4) + 2 f(4) + 2 = [(4)2 – 5] + 2
= [16 – 5] + 2 = 11 + 2
f(4) + 2 = 13
Ex. 2 If f(x) = x2 – 5, find the following: