00:01
So in this question, we say if f of x is equal to x cubed and g of x is equal to negative 2x cubed, how has f of x been transformed to get g of x? so let's go to a calculator and that will help us see what's happening here.
00:16
So what i've done here is i've gone to a graph in calculator, and in y1 here in blue, i'm looking at the graph of x cubed.
00:26
And in y2 in red, i'm going to have negative 2x cubed.
00:32
So in this question, we're really asking, how did we get from the blue graph, which is f of x equals x cubed, to the red graph, and my red graph this time is g of x equals negative 2 x cubed.
00:52
So let's see here.
00:54
If i look at my options, okay, notice first of all that the first two options talk about us shifting f of x shifting the blue function either up or down, right? and if i take a look at the blue and the red function here, it doesn't look like we've done any shifting up or down.
01:16
We've done some reflecting, it looks like, but not any shifting up or down.
01:21
And so the first two answer choices are not going to be correct this time.
01:27
If you look at the second two answer choices, they talk about reflections and shifting left, or right.
01:35
Did i do any movement left or right this time? it really doesn't look like it, right? looks like we did some reflection and maybe a little stretching or something, but we didn't move the graph fundamentally either left or right, and so those second two options, they aren't correct either.
01:55
My last question or my last option here says the graph of f of x has been reflected across the y axis and shifted by a factor of 2, and stretched, i should say, by a factor of 2.
02:09
And that is correct...