Complete the table of values for the function f(x) = (1/3)x for a, b, and c. x : -2, -1, 0, 1, 2. f(x) : a, b, c, 1/3, 1/9
balu736 [363]
Given:
The function is
![f(x)=\left(\dfrac{1}{3}\right)^x](https://tex.z-dn.net/?f=f%28x%29%3D%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5Ex)
To find:
The missing values for a, b, and c in the given table.
Solution:
We have,
![f(x)=\left(\dfrac{1}{3}\right)^x](https://tex.z-dn.net/?f=f%28x%29%3D%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5Ex)
At x=-2,
![f(-2)=\left(\dfrac{1}{3}\right)^{-2}](https://tex.z-dn.net/?f=f%28-2%29%3D%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5E%7B-2%7D)
![\left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbecause%20%5Cleft%28%5Cdfrac%7Ba%7D%7Bb%7D%5Cright%29%5E%7B-n%7D%3D%5Cleft%28%5Cdfrac%7Bb%7D%7Ba%7D%5Cright%29%5E%7Bn%7D%5Cright%5D)
![a=9](https://tex.z-dn.net/?f=a%3D9)
At x=-1,
![f(-1)=\left(\dfrac{1}{3}\right)^{-1}](https://tex.z-dn.net/?f=f%28-1%29%3D%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5E%7B-1%7D)
![\left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbecause%20%5Cleft%28%5Cdfrac%7Ba%7D%7Bb%7D%5Cright%29%5E%7B-n%7D%3D%5Cleft%28%5Cdfrac%7Bb%7D%7Ba%7D%5Cright%29%5E%7Bn%7D%5Cright%5D)
![b=3](https://tex.z-dn.net/?f=b%3D3)
At x=0,
![f(0)=\left(\dfrac{1}{3}\right)^{0}](https://tex.z-dn.net/?f=f%280%29%3D%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5E%7B0%7D)
![\left[\because a^0=1, a\neq 0\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbecause%20a%5E0%3D1%2C%20a%5Cneq%200%5Cright%5D)
Therefore, the missing values of a,b and c are 9, 3, and 1 respectively.
Answer:
Step-by-step explanation:
(Y1 +Y2)/2=-7+3/2 so y=-2
(X1 +X2)/2=4+2/2 so x=3
Step-by-step explanation:
Fahd fhnkynmkfufudhdbxbcjhdhdhxxb
Answer:
40-x-15= 19
x will equal 6
Step-by-step explanation: