Final answer:
To plot points on a graph with the given domain {1/2, 1, 2, 4, 8} and y=log₂x, calculate log₂ for each x-value to determine the y-value. Plot these on the graph, noting the trend that log(x) increases as x increases, but at a decreasing rate on a logarithmic scale.
Step-by-step explanation:
The student is asked to plot data points on a graph with the given domain {1/2, 1, 2, 4, 8} where the y-axis represents the logarithm with base 2 (log₂x). To plot these points, we first calculate the logarithm of each x-value in the domain. The graph will show a trend that, as x increases, the log(x) value increases, but at a decreasing rate due to the properties of logarithms on a logarithmic scale.
- For x = 1/2, log₂(1/2) = -1
- For x = 1, log₂(1) = 0
- For x = 2, log₂(2) = 1
- For x = 4, log₂(4) = 2
- For x = 8, log₂(8) = 3
Each computed y-value should be plotted against its corresponding x-value from the domain on the graph. In this case, the graph should have a horizontal red line representing the x-axis and will display a curve that rises more slowly as x increases. This captures the essence of how the frequency of the y-value changes in relation to x on a logarithmic scale.