Question

the graph above is a transformation of the function x^2.
Give the function in the graph above.
g(x)=

Answer 1

To determine the function \( g(x) \) which is a transformation of the basic quadratic function \( f(x) = x^2 \), we would need more specific information about the transformations applied. Transformations can include shifting, stretching, compressing, or reflecting the graph.

Here are some common transformations and how they affect the function:

1. **Vertical Shift**: \( g(x) = x^2 + k \) (shifts the graph up by \( k \) units if \( k > 0 \) and down if \( k < 0 \)).
2. **Horizontal Shift**: \( g(x) = (x - h)^2 \) (shifts the graph right by \( h \) units if \( h > 0 \) and left if \( h < 0 \)).
3. **Vertical Stretch/Compression**: \( g(x) = a \cdot x^2 \) (stretches if \( |a| > 1 \) and compresses if \( 0 < |a| < 1 \); reflects over the x-axis if \( a < 0 \)).
4. **Horizontal Stretch/Compression**: \( g(x) = (bx)^2 \) (stretches if \( 0 < |b| < 1 \) and compresses if \( |b| > 1 \)).

If you can describe the specific transformation (such as shifts, stretches, or reflections) that occurred to the graph of \( x^2 \), I can assist you in determining the exact form of \( g(x) \). Alternatively, if you can provide a visual representation or values of specific points, I can help analyze the transformation further.