To draw the graph of y = -h(x) + 3, we need to reflect the graph of y = h(x) across the x-axis and then shift it upward by 3 units.
1. Start by plotting the points on the graph of y = h(x) and connect them to form a smooth curve.
2. Reflect the graph across the x-axis by changing the sign of the y-coordinates. For example, if a point on the original graph is (x, y), the corresponding point on the new graph will be (x, -y).
3. Shift the reflected graph upward by 3 units. Add 3 to the y-coordinate of each point on the reflected graph.
4. Connect the points on the reflected and shifted graph to form a smooth curve.
To draw the graph of y = 2g(x+4), we need to stretch the graph of y = g(x) vertically by a factor of 2 and shift it horizontally 4 units to the left.
1. Start by plotting the points on the graph of y = g(x) and connect them to form a smooth curve.
2. Stretch the graph vertically by multiplying the y-coordinates by 2. For example, if a point on the original graph is (x, y), the corresponding point on the new graph will be (x, 2y).
3. Shift the graph horizontally 4 units to the left by subtracting 4 from the x-coordinate of each point.
4. Connect the points on the stretched and shifted graph to form a smooth curve.
Remember to label the axes and provide appropriate scales to accurately represent the graphs.