Final answer:
Changing the function f(x) = x2 to 7f(x) results in a vertical stretch of the graph, making the y-values 7 times larger and causing a steeper-looking parabola.
Step-by-step explanation:
When the function f(x) = x2 is changed to 7f(x), which means it becomes 7x2, the effect on the graph is a vertical stretch. This is because the value of the function at every point x is multiplied by 7, which makes the y-values 7 times larger than before. There is no change in the x-values, which means there is no horizontal stretching or compression. This transformation results in a steeper-looking parabola.
A real-world analogy of this vertical stretching can be observed when comparing the scale on a vertical axis. In graphic representations, changing the scale to a wider range makes fluctuations appear smaller, similar to a vertical compression. In contrast, a steeper scale makes fluctuations seem larger, analogous to a vertical stretch as with our function 7x2