#7. The graph of fx=x2is shown on the grid. Which statement about the relationship between the graph of fand the graph of g(x)=5x2 is true?

To analyze the relationship between the graph of \( f(x) = x^2 \) and the graph of \( g(x) = 5x^2 \), we need to consider the transformations involved.

The function \( g(x) = 5x^2 \) can be seen as a vertical scaling of the function \( f(x) = x^2 \).

Here’s a step-by-step breakdown:

1. **Original Function \( f(x) = x^2 \)**: This is a parabola that opens upwards with its vertex at the origin (0, 0). The standard form of the quadratic function \( y = x^2 \) is well known, where the graph is a symmetrically shaped curve.

2. **Transformed Function \( g(x) = 5x^2 \)**: This transformation involves multiplying the \( x^2 \) term by 5.

### Effects of the Transformation:

- **Vertical Stretch**: Multiplying by a constant \( A > 1 \) will stretch the graph vertically.
- **No Horizontal Change**: The shape and location of the parabola in the horizontal axis remain unchanged.
- **Steeper Curve**: For \( g(x) = 5x^2 \), the parabola will be steeper than \( f(x) = x^2 \). Points on the graph of \( g(x) \) will be higher than those on the graph of \( f(x) \) for any \( x \neq 0 \).

### More Specifically:
- For \( x = 1 \):
- \( f(1) = 1^2 = 1 \)
- \( g(1) = 5 \times 1^2 = 5 \)
- For \( x = 2 \):
- \( f(2) = 2^2 = 4 \)
- \( g(2) = 5 \times 2^2 = 20 \)

### Conclusion:
The statement about the relationship between the graph of \( f(x) = x^2 \) and \( g(x) = 5x^2 \) that is true is:

"The graph of \( g(x) = 5x^2 \) is a vertical stretch of the graph of \( f(x) = x^2 \) by a factor of 5."

In other words, for each value of \( x \), the corresponding \( y \)-value on the graph of \( g(x) = 5x^2 \) is 5 times the \( y \)-value on the graph of \( f(x) = x^2 \).

so what is the answer

The answer to the question, "Which statement about the relationship between the graph of \( f(x) = x^2 \) and the graph of \( g(x) = 5x^2 \) is true?" is:

"The graph of \( g(x) = 5x^2 \) is a vertical stretch of the graph of \( f(x) = x^2 \) by a factor of 5."

This means that for every \( x \) value, the \( y \) value in the graph of \( g(x) = 5x^2 \) is 5 times the \( y \) value in the graph of \( f(x) = x^2 \). As a result, the parabola represented by \( g(x) \) is steeper than the parabola represented by \( f(x) \).