Question

Write the function with the given transformation from the given parent function
reflected across the x-axis
vertically stretched by a factor of 5
shifted up 7

Answer 1

If the parent function is y = f(x), apply the transformations in order:

- Reflect across the x-axis: multiply by −1 → −f(x)
- Vertically stretch by factor 5: multiply by 5 → −5f(x)
- Shift up 7: add 7 → −5f(x) + 7

So the transformed function is y = −5f(x) + 7.

Examples:
- If f(x) = x^2, y = −5x^2 + 7.
- If f(x) = |x|, y = −5|x| + 7.
- If f(x) = √x, y = −5√x + 7.