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The function graphed with a solid line is the parent function y=f(x) with a vertex of (9,9) points (-1,1), (1,1)

The dotted line y= 4f(x) with points (0,0),(-1,4) and (1,4)describe the transformed function
The parent function has been vertically stretched by a factor 1/4
Vertically compressed by a factor of 4
Vertically stretched by a factor of 4
Vertically compressed y a factor of 1/4

1 answer

To analyze the transformations that have taken place based on the given information:

  1. Understanding the Parent Function: The parent function \( y = f(x) \) has a vertex of (9, 9) and includes the points (-1, 1) and (1, 1).

  2. Transformed Function: The transformed function is described as \( y = 4f(x) \).

Transformation Analysis:

  • The transformation \( y = 4f(x) \) indicates a vertical stretch by a factor of 4.
    • This is because when you multiply the output of a function by a factor greater than 1, the graph stretches away from the x-axis.

Summary of Options:

  • Vertically stretched by a factor of 4: Correct, the transformed function \( y = 4f(x) \) indicates this.
  • Vertically compressed by a factor of 4: Incorrect, this implies a multiplication by a factor less than 1.
  • Vertically stretched by a factor of 1/4: Incorrect, this also implies reducing the height of the graph.
  • Vertically compressed by a factor of 1/4: Incorrect, as this implies decreasing the height of the graph as well.

Conclusion:

Thus, the correct answer is: Vertically stretched by a factor of 4.