00:01
In part a, we write a function formula for the function g using the function f.
00:05
So let's replace the graph of the function f first.
00:10
The first thing that we have to do on the graph of f is we have to reflect it over the x axis.
00:18
When we reflected over the x axis, we are going to get a graph like this.
00:23
And then we have to move this graph to the left by three units because we see that after reflecting over the x -axis, the vertex is at 0, 0, that is at origin.
00:37
And after translating to the left by 3 units, the vertex is going to be at negative 3.
00:46
So here we see two graph transformation.
00:50
The first one is reflection over x -axis.
00:57
And then the second one is horizontal translation and this is to the left by three units.
01:25
Now let's write the function equivalent of these two graph transformation.
01:30
Since we start from the graph of f, when you reflect the graph of f over the x axis, this is equivalent to negative of f of x.
01:40
And then from here, this one is basically negative of f of x.
01:44
We shift this graph to the left by 3 units.
01:48
So according to graph transformation, this is equivalent to negative of f of x plus 3.
01:56
And this basically equals the graph of g.
02:00
So we write g of x equals negative of f of x plus 3...