graph Y=log3(x+1) graph Y<log2 ^X
We can't draw graphs for you here.
To graph the inequality Y < log₂ (x), we follow these steps:
1. Start by graphing the equation Y = log₂ (x). This will be our baseline graph.
For the baseline graph:
- Choose some x-values to evaluate the function. Let's pick x = 1, 2, 4, and 8.
- Plug these x-values into the equation Y = log₂ (x) to find the corresponding y-values.
- Plot the points (x, y) on the graph.
- Connect the plotted points with a smooth curve. Remember that the graph of log functions starts at (1, 0).
2. Next, we need to shade the region below the graph of Y = log₂ (x) to satisfy the inequality Y < log₂ (x).
To shade the region:
- Choose any point outside the shaded area, for example, (0, 0).
- Substitute the x and y coordinates of this point into the inequality Y < log₂ (x).
- If the inequality holds true, shade the region below the baseline graph. Otherwise, shade the region above the baseline graph.
This method ensures that any point in the shaded region will satisfy Y < log₂ (x).
Please note that we are unable to draw the graph for you in this text-based format. However, following these steps should help you graph the inequality Y < log₂ (x) on your own.