00:01
This problem wants us to graph the basic function f of x equals absolute value of x, then describe the sequence of transformations for our g of x function, which will be our red function here.
00:11
And then we will also graph both functions on the same grid so we can see the transformations taking place.
00:17
So first for our f of x equals absolute value of x function, we start with our vertex point, which is assumed to be zero zero unless we have transformations.
00:25
And to create the absolute value function, what we are doing is creating lines basically on both sides that have a rate of one and negative one or a slope of one and negative one.
00:37
And the way we can make those points is by going up one and right one, up one and right one a few times for the right side of our absolute value.
00:45
Then we also go up one left one, which would create a negative slope over and over again for the left side of our absolute value.
00:52
So like we said, it's almost like two linear functions meeting at our vertex, one with a positive slope and one with a negative slope.
01:00
Now for our g of x function we're going to see four transformations.
01:05
First, the negative in front of the two gives us a vertical reflection.
01:09
The two also gives us a vertical stretch and then we have a transformation of vertical and horizontal translations and certain directions and what we're going to see is that our vertex is going to shift from zero zero to being positive one positive three because x minus one gives us a shift right one and the positive three gives us a vertical shift up three.
01:32
So if we go write one up three, that will give us our new vertex for this g of x function.
01:39
And if it wasn't for the negative and the two, we would make the same movements and same points we did for the f of x original function.
01:47
But there's two things we need to change...