Answer:
To determine the transformation of a parent function, you can rewrite the function by identifying any changes applied to the parent function. Here is a general step-by-step process:
1. Identify the parent function: Start by identifying the parent function, which is typically a basic function without any modifications or transformations.
2. Determine the changes applied: Look for any modifications to the parent function. These changes can include shifts, stretches or compressions, reflections, and changes to the vertical or horizontal scales.
3. Rewrite the function: Based on the identified changes, rewrite the function by incorporating the necessary transformations. These transformations will affect specific elements of the function, such as coefficients, exponents, and variables.
Now, let's discuss how to describe the transformation of the graph compared to the parent function. When comparing the transformed graph to the parent function, you need to consider the following:
1. Vertical transformations: If the function has been vertically shifted upwards or downwards, describe the amount and direction of the shift.
2. Horizontal transformations: If the function has been horizontally shifted to the left or right, describe the amount and direction of the shift.
3. Stretching or compression: If the function has been stretched vertically or compressed vertically, describe whether the graph has become narrower or wider compared to the parent function.
4. Reflection: If the function has been reflected across the x-axis or y-axis, describe the axis of reflection and how it has affected the graph.
5. Changes in amplitude or period: If the function represents a periodic function (such as sine or cosine), describe any changes in amplitude (vertical scaling) or period (horizontal scaling) compared to the parent function.
By analyzing these aspects, you can provide a detailed description of the transformation of the graph in relation to the parent function.