logarithmic function table completion

1. Understand the function: The given function is $y = \log_{2} x$. This means that $y$ is the exponent to which the base $2$ must be raised to get $x$. In other words, $2^{y} = x$.

1. Calculate for $x = 1$: Substitute $x = 1$ into the equation: $y = \log_{2} 1$. Since $2^{0} = 1$, we have $y = 0$.

1. Calculate for $x = 2$: Substitute $x = 2$ into the equation: $y = \log_{2} 2$. Since $2^{1} = 2$, we have $y = 1$.

1. Calculate for $x = 4$: Substitute $x = 4$ into the equation: $y = \log_{2} 4$. Since $2^{2} = 4$, we have $y = 2$.

5. Summary of results: The completed table is:
| $x$ | $y$ |
|---|---|
| 1 | 0 |
| 2 | 1 |
| 4 | 2 |

1. Identify the graph: A graph representing $y = \log_{2} x$ must pass through the points $(1, 0)$, $(2, 1)$, and $(4, 2)$. It will be an increasing curve that passes through $(1, 0)$ and approaches the y-axis (the line $x=0$) as an asymptote.