Answer:
[tex]g(x) = (x-a,-y - b)[/tex]
Step-by-step explanation:
Given
Represent f(x) as follows:
[tex]f(x) = (x,y)[/tex]
Transformations:
Horizontally shifted right by a
Reflected across x axis
Vertically shifted down by b
Taking the transformations one after the other.
Horizontally shifted right by a
When a function is shifted right, the resulting function is:
[tex]f' = (x-a,y)[/tex]
Reflected across x axis
Here, the x axis remains unaltered while the y axis is negated
[tex]f' = (x-a,y)[/tex]
becomes
[tex]f" = (x-a,-y)[/tex]
Vertically shifted down by b
When a function is shifted down by b, the resulting function is:
[tex]f"' = f" - b[/tex]
i.e, subtract b from the function (f(x) or y, as the case may be)
So, we have:
[tex]f"' = (x-a,-y - b)[/tex]
Represent f"' with g(x)
[tex]g(x) = (x-a,-y - b)[/tex]
