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vodomira [7]
3 years ago
15

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
Mathematics
1 answer:
Sveta_85 [38]3 years ago
3 0

Answer:

g(x) = (x-a,-y - b)

Step-by-step explanation:

Given

Represent f(x) as follows:

f(x) = (x,y)

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:

f' = (x-a,y)

Reflected across x axis

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

f' = (x-a,y)

becomes

f" = (x-a,-y)

Vertically shifted down by b

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

f"' = f" - b

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

So, we have:

f"'  = (x-a,-y - b)

Represent f"' with g(x)

g(x) = (x-a,-y - b)

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