00:01
This question gives you a statement and asks if it's true or false.
00:05
The statement that it gives is that if you have the graphs or the functions f of x equals 3 to the negative x, and g of x equals negative 3 to the x, then these will have the same graph.
00:24
Well, let's think about this for a second.
00:26
We know that the graph of 3 to the x looks like this.
00:34
If we have our axes here, it's a standard exponential curve, which starts low and goes up like this.
00:43
What happens when we multiply that by negative? when we make this whole thing negative, we know that that will flip over the x -axis.
00:54
So what was once a positive y is now a negative y.
00:58
That'll look something like this.
01:02
It'll be the same thing reflected over the x -axis.
01:08
So what happens now when we make the exponent negative instead of the whole thing negative? well, when we make the exponent negative, or in this instance when we're making the independent variable negative, instead of flipping over the x -axis like we did with g, instead we flip over the y -axis.
01:30
That's because when we have a positive x over here, it's being treated in the function like a negative x...