Given the function f(x) = x
We will find the function g(x) whose graph is produced by the following transformations on the graph of f(x)
First, The graph of f is reflected vertically
So,
[tex]\begin{gathered} f(x)\rightarrow f(-x) \\ g(x)=-x \end{gathered}[/tex]Second, expanded horizontally by a factor of 2
So,
[tex]\begin{gathered} f(-x)\rightarrow f(-2x) \\ g(x)=-2x \end{gathered}[/tex]Finally, shifted right 6 units, and shifted down 4 units.
So,
[tex]\begin{gathered} f(-2x)\rightarrow f(-2(x-6))-4 \\ g(x)=-2(x-6)-4 \end{gathered}[/tex]Simplifying the function g(x):
[tex]g(x)=-2x+8[/tex]The graph of the function (f) and (g) will be as shown in the following figure:
