To determine the relationship between the graphs of \( f(x) = x^2 \) and \( g(x) = 5x^2 \), we need to analyze the transformation applied to \( f(x) \) to obtain \( g(x) \).
1. **Different Coefficient's Effect**:
- The general form of a quadratic function is \( f(x) = ax^2 \).
- If the coefficient \( a \) is greater than 1, the graph of the quadratic function becomes narrower (vertically stretched).
- If the coefficient \( a \) is between 0 and 1, the graph becomes wider (vertically compressed).
- If \( a \) is negative, there is also a reflection over the x-axis, but in this case, \( a = 5 \), which is positive and greater than 1.
2. **Comparing the Given Functions**:
- For \( f(x) = x^2 \), the coefficient \( a \) is 1.
- For \( g(x) = 5x^2 \), the coefficient \( a \) is 5, which is greater than 1.
Due to the coefficient 5 in \( g(x) = 5x^2 \), the graph of \( g \) is vertically stretched compared to \( f \), making it narrower.
Thus, the correct statement is:
- The graph of \( g \) is narrower than the graph of \( f \).
The graph of `f\left(x\right)=x^{2}`is shown on the grid. Which statement about the relationship between the graph of `f`and the graph of `g(x)=5x^{2}` is true?
the graph of g is narrower than the graph of f
the graph of g is wider then the graph of f
the graph of g is 5 units below the graph of f
the graph of g is 5 units above the graph of f
1 answer