The graph of y - 2g(x) - 1 is obtained by applying vertical stretching, reflection, and vertical translation to the original function g(x). The transformed points are (0, -1), (-2, -9), and (4, -5).
To draw the graph of y - 2g(x) - 1, we first need to understand the transformations applied to the original function g(x). The given coordinates (0, 0), (-2, -4), and (4, -2) correspond to points on the graph of g(x).
Now, consider the expression y - 2g(x) - 1. This involves subtracting twice the values of g(x) from y and then subtracting 1. This process suggests vertical stretching, reflection, and vertical translation.
Starting with the points on g(x), let's apply these transformations:
Vertical Stretching: The factor of 2 before g(x) indicates vertical stretching by a factor of 2.
Reflection: The subtraction of 2g(x) reflects the graph over the x-axis.
Vertical Translation: Finally, subtracting 1 shifts the graph downward by 1 unit.
Applying these transformations to the given points, we get the transformed coordinates: (0, -1), (-2, -9), and (4, -5).
Now, plot these transformed points on the graph. Connect the points smoothly to represent the new function y - 2g(x) - 1.