Answer: if you multiply the f(x) by 1/4 the graph seems to narrow, which is interpreted as a positive vertical shift . The y value (output) is 4 times greater
If you multiply the x² by 1/4, the graph seems to widen, which is interpreted as a negative vertical shift. The y value is less by a factor of 1/4
Step-by-step explanation: I am reading the question literally: multiplying f(x) by 1/4. (This may be dangerous as mathematicians have their own lingo, and some words have specialized meanings that English majors haven't learned!)
I understand that f(x) or any other function is the y-output. So in order to graph a function, it is legitimate to substitute "y" for f(x).
I am attaching a graph with the f(x)=x² in red f(x) = (1/4)x² in green and (1/4)f(x) = x² in blue.
As you can see, very different results: Substituting 2 for x
in red original 4 = 2²
in green f(x) = (1/4)(2²) . 1 = (1/4)(4)
in blue (1/4)f(x) = x² (1/4) 16 = (2²) =. This is probably not the intended result, but it is literally what happens if you multiply the left side! 16 is the output on the graph.
So, despite my efforts to make sense of this, I realize that this answer is mistaken, and I hope someone can clear up my confusion, please!