Answer:
The table can be filled as shown below.
Step-by-step explanation:
The first function is
![f(x)=4x+8](https://tex.z-dn.net/?f=f%28x%29%3D4x%2B8)
Put different values of x and find values of f(x).
For x=-2
![f(-2)=4(-2)+8=0](https://tex.z-dn.net/?f=f%28-2%29%3D4%28-2%29%2B8%3D0)
For x=-1
![f(-1)=4(-1)+8=4](https://tex.z-dn.net/?f=f%28-1%29%3D4%28-1%29%2B8%3D4)
Similarly for x=0,1,2 the value of f(x) are 8,12,16 respectively.
The second function is
![f(x)=\frac{2}{3}x+8](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B2%7D%7B3%7Dx%2B8)
For x= -6
![f(-6)=\frac{2}{3}(-6)+8=4](https://tex.z-dn.net/?f=f%28-6%29%3D%5Cfrac%7B2%7D%7B3%7D%28-6%29%2B8%3D4)
For x= -3
![f(-3)=\frac{2}{3}(-3)+8=6](https://tex.z-dn.net/?f=f%28-3%29%3D%5Cfrac%7B2%7D%7B3%7D%28-3%29%2B8%3D6)
Similarly for x=0,3,6 the value of f(x) are 8,10,12 respectively.
The third function is
![f(x)=5^{x-2}+7](https://tex.z-dn.net/?f=f%28x%29%3D5%5E%7Bx-2%7D%2B7)
For x= 2
![f(2)=5^{2-2}+7=8](https://tex.z-dn.net/?f=f%282%29%3D5%5E%7B2-2%7D%2B7%3D8)
For x= 3
![f(3)=5^{3-2}+7=12](https://tex.z-dn.net/?f=f%283%29%3D5%5E%7B3-2%7D%2B7%3D12)
Similarly for x=4,5,6 the value of f(x) are 32,132,632 respectively.
The fourth function is
![f(x)=(\frac{1}{4})^x-5](https://tex.z-dn.net/?f=f%28x%29%3D%28%5Cfrac%7B1%7D%7B4%7D%29%5Ex-5)
For x=-4
![f(-4)=(\frac{1}{4})^{-4}-5=4^4-5=251](https://tex.z-dn.net/?f=f%28-4%29%3D%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B-4%7D-5%3D4%5E4-5%3D251)
For x=-3
![f(-3)=(\frac{1}{4})^{-3}-5=4^3-5=59](https://tex.z-dn.net/?f=f%28-3%29%3D%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B-3%7D-5%3D4%5E3-5%3D59)
Similarly for x=-2,-1,0 the value of f(x) are 11,-1,-4 respectively.