by Guest » Thu May 21, 2020 1:44 pm
Do you not know the basic rules of logarithms?
log(ab)= log(a)+ log(b) and log(a/b)= log(a)- log(b).
So log(2/x)= log(2)- log(x).
Further, since this logarithm is "base 2", log(2)= 1 so
this is 1- log(x).
The rest involves calculating values.
2^0= 1 so log(1)= 0. With y(x)= log(2/x)= 1- log(x), y(0)= 1- 0= 1.
2^1= 2 so log(2)= 1. y(2)= 1- 1= 0.
2^2= 4 so log(4)= 2. y(4)= 1- 2= -1
2^3= 8 so log(8)= 3. y(8)= 1- 3= -2
For negative x, 2^{-1}= 1/2 so log(1/2)= -1. y(1/2)= 1-(-1)= 2
2^{-2}= 1/4 so log(1/4)= -2. y(1/4)= 1- (-2)= 3.
Mark the points (1/4, 3), (1/2, 2), (0, 1), (2, 0), (4, -1), (8, -2) and draw a smooth curve through them. Do you see that x= 0 will be a vertical asymptote?