Final answer:
The transformation involved is a horizontal stretch, as the coefficient of the x^2 term in g(x) is 9 times larger than in f(x), causing the parabola to spread out more along the x-axis while keeping the same vertical shift.
Step-by-step explanation:
The transformation that converts the graph of f(x)=x^2–9 into the graph of g(x)=9x^2–9 is a horizontal stretch. To see why, let's compare the two equations. The function f(x) is a standard parabola centered at the origin, which has been shifted vertically downward by 9 units due to the –9 term.
When we look at g(x), the coefficient of x^2 has been changed from 1 (in f(x)) to 9 (in g(x)). This multiplication by 9 of the x^2 term causes the parabola to stretch horizontally, meaning that for a given y-value (except for the vertex at y=-9), the absolute value of the corresponding x-values will be greater in the graph of g(x) than in the graph of f(x). The negative sign in front of the 9 term remains the same, indicating that there is no reflection across the x-axis or y-axis, as both parabolas open upwards and are shifted down by the same amount.