Question

Using the graph below, what transformation occurred to the parent function in red?
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2 points
Captionless Image
Reflection over the x-axis
Reflection over the y-axis
Dilation 0f 4
Translation of -4

Answer 1

To determine the transformation of the parent function in the graph, we need to analyze the given options based on the common transformations applied to functions:

1. **Reflection over the x-axis**: This transformation occurs when the function is multiplied by -1 (e.g., f(x) becomes -f(x)). The graph will appear inverted compared to the parent function.

2. **Reflection over the y-axis**: This transformation occurs when the input variable is negated (e.g., f(x) becomes f(-x)). The graph is flipped horizontally.

3. **Dilation of 4**: This implies the function is stretched vertically or horizontally by a factor of 4. Generally, this would look like f(x) becomes 4f(x) for a vertical stretch or f(x) becomes f(4x) for horizontal compression.

4. **Translation of -4**: This means the graph has been shifted horizontally or vertically, often specified as shifting left or right (e.g., f(x) becomes f(x + 4) which is a shift left).

Since I can't see the graph, here's how you can determine the transformation:

- Check if the graph is inverted relative to the parent function; this indicates a reflection over the x-axis.
- Check if the graph is flipped horizontally; this indicates a reflection over the y-axis.
- If the graph looks much wider or narrower than the parent function, consider if it is a dilation.
- If the entire graph has moved left or right with respect to the parent function, then it is translated.

Please compare these transformations with the graph to identify which option applies.