The graph of y = 3(x + 1) is a vertical stretch of the graph of y = x + 1 by a factor of 3 and a translation of 1 unit to the left.
To see why, let's rewrite y = 3(x + 1) as y = 3x + 3. This equation has the same slope as y = x + 1, which is 1. However, the y-intercept is different. For y = x + 1, the y-intercept is (0, 1), while for y = 3x + 3, the y-intercept is (0, 3). This means that the graph of y = 3x + 3 is shifted vertically upward by 2 units compared to the graph of y = x + 1.
Next, let's look at how the graph of y = 3x + 3 is stretched vertically compared to the graph of y = x + 1. The factor of 3 in front of the parentheses in y = 3(x + 1) means that the y-coordinate of each point on the graph of y = x + 1 is multiplied by 3. This stretches the graph vertically by a factor of 3.
So, in summary, the graph of y = 3(x + 1) is the graph of y = x + 1 shifted 1 unit to the left and stretched vertically by a factor of 3.