Suppose that the function LaTeX: f(x) f ( x ) is shifted horizontally to the right by LaTeX: a a , reflected across the LaTeX: x x -axis, and shifted vertically down by LaTeX: b b to become the function LaTeX: g(x) g ( x ) . Write the function LaTeX: g(x) g ( x ) in terms of LaTeX: f(x) f ( x ) and explain each of the shifts

Step-by-step explanation:

Given

Represent f(x) as follows:

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:

Reflected across x axis

Here, the x axis remains unaltered while the y axis is negated

becomes

Vertically shifted down by b

When a function is shifted down by b, the resulting function is:

i.e, subtract b from the function (f(x) or y, as the case may be)

So, we have:

Represent f"' with g(x)

step-by-step explanation:

see if this :

step-by-step explanation: