Answer:
To transform the parent graph y = x into a new graph, several transformations can be applied. The transformations that can be used to obtain the desired graph are:
1. Horizontal translation: This transformation involves shifting the graph horizontally by adding or subtracting a constant value to the x-coordinate of each point on the graph. If a positive value is added, the graph will shift to the left, and if a negative value is added, it will shift to the right.
2. Vertical compression: This transformation involves compressing or stretching the graph vertically by multiplying the y-coordinate of each point on the graph by a constant value less than 1. This causes the graph to become narrower or compressed vertically.
3. Reflection in the x-axis: This transformation involves flipping the graph upside down by changing the sign of each y-coordinate. The x-coordinates remain unchanged.
4. Vertical translation: This transformation involves shifting the graph vertically by adding or subtracting a constant value to the y-coordinate of each point on the graph. If a positive value is added, the graph will shift upward, and if a negative value is added, it will shift downward.
5. Reflection in the y-axis: This transformation involves flipping the graph horizontally by changing the sign of each x-coordinate. The y-coordinates remain unchanged.
In summary, to transform the parent graph y = x into a new graph, one can use horizontal translation, vertical compression, reflection in the x-axis, vertical translation, and reflection in the y-axis.
Explanation: