The graph of f(x)=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?
Both graphs have the same shape, but the graph of g is steeper than the graph of f.
The graph of f(x) = x^2 is a parabola that opens upward, with its vertex at the origin (0,0).
To compare it with the graph of g(x) = 5x^2, we need to consider the effect of the coefficient 5.
When we multiply the function f(x) by a positive constant, such as 5, it scales the graph vertically. In this case, since the coefficient is 5, the graph of g(x) = 5x^2 will be steeper and narrower than f(x). The vertex of g(x) will remain at the origin (0,0), but the y-values of the graph will be stretched by a factor of 5 compared to f(x).
Therefore, the statement that is true about the relationship between the graph of f(x) = x^2 and g(x) = 5x^2 is that the graph of g(x) is steeper and narrower than the graph of f(x).