Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x)...
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Transcript of Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x)...
![Page 1: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/1.jpg)
Warm Up Exercise…Find the range of the function with the
given domain (x) – {-2, 0, 3.5}f(x) = (-2x)(-2x)
g(x) = 10 – (x)(x)(x)
y = 5x – 1
![Page 2: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/2.jpg)
Lesson #8.1
Zero & Negative Exponents
SWBAT simplify expressions with zero and negative exponents; evaluate exponential
expressions.
Concept: UNIT 8
![Page 3: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/3.jpg)
22 Means… 2 • 2 = 4 21 Means… 2 = 2
20 Means… 1
What does 2-1 Mean?
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
![Page 4: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/4.jpg)
What does 2-1 Mean? You cannot leave an exponent
negative because there is NO WAY to express it’s meaning.
You must make it positive!
11 12
2
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
![Page 5: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/5.jpg)
You do NOT want to have negative exponents in your answer. You get rid of them by flipping the exponent over, like reciprocals.
2 5 15 2 If the negative exponent
is on top, move it to the bottom.
22
122
22
1 22 1
4 4
1
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
![Page 6: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/6.jpg)
Definition of Negative ExponentFor any integer n, a-n is the reciprocal of an
1n
naa
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
![Page 7: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/7.jpg)
Definition of Negative ExponentFor any integer n, a-n is the reciprocal of an
11 12
2
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
![Page 8: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/8.jpg)
Definition of Negative ExponentFor any integer n, a-n is the reciprocal of an
22
1( 5)( 5)
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
![Page 9: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/9.jpg)
Simplify.11) 3
23) 5
22) 4
24) 6
13
215
125
214
116
216
136
A negative exponent is an inverse!1x 1
xFlip the number over to make the exponent positive!
1 1
1 1
8.1 – Zero & Negative Exponents8.1 – Zero & Negative Exponents
![Page 10: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/10.jpg)
Zero Exponent:
Negative Exponent:
0 1a 1n
naa
RULE: YOU SHOULD NEVERNEVER HAVE A NEGATIVE EXPONENT AS YOUR FINAL
ANSWER
8.1 – Zero & Negative Exponents
![Page 11: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/11.jpg)
01) 6
Simplify.
02) -2
03) 9 04) 5 20 8
1 1
1 1
0 1x
8.1 – Zero & Negative Exponents
![Page 12: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/12.jpg)
8.1 – Zero & Negative Exponents
Simplify the following:a. 3 c. (-4)
b. (-8.1) d. (2.45678913)
-2 -5
0 0
![Page 13: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/13.jpg)
1n
naa
25) 12 26) 7 21
121
1442
17
149
Simplify.
1 1
8.1 – Zero & Negative Exponents
![Page 14: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/14.jpg)
8.1 – Zero & Negative Exponents
Simplifya. 11m b. 7s - 4t
c. d.
-5 2
3
2a 2
5
vn
![Page 15: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/15.jpg)
Simplify the following expressions:
2
3
5
0
41.4
.3
1.2
6.1
ghx
7
4
5
0
6
3
.8
7.
0) zfor (.6
.5
tr
xy
z
pn
3hg
1
x5
16
-n3p6
1
55
1yx
4
7
rt
![Page 16: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/16.jpg)
Practice Problems
1. 2-2
¼
2. (-2)0
13. 5-x
1/5x
4. (½)-1 2
5. 5(2-1)5/2
6. 2x-2y-3
2/y3x2
![Page 17: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/17.jpg)
More Practice
7. x-5
1/x5 8.
x5/29. x4y-7
x4/y7
10.
x3y/9
521
x
1391
yx
![Page 18: Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5} f(x) = (-2x)(-2x) g(x) = 10 – (x)(x)(x) y = 5x – 1.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1af27f8b9ab05997f4c4/html5/thumbnails/18.jpg)
8.1 – Zero & Negative Exponents
Evaluate each expression for n = -2 and w = 5
a. n w b. c. d. 2
1
wn
4
0
nw
2
1nw
-3 0