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15 votes
15 votes
The graph of f(x) is given below. State the

order of the transformation occurring in
g(x) = f(-x-1) + 3 and sketch the graph
of g(x).

The graph of f(x) is given below. State the order of the transformation occurring-example-1
User Mirjalal
by
2.6k points

1 Answer

21 votes
21 votes

Answer:

  • translation right 1 and up 3
  • reflection over the y-axis
  • see the attachment for a graph

Explanation:

You want the sequence of transformations occurring to form g(x) = f(-x-1) +3.

Translation

Translation of f(x) by h units right and k units up is accomplished by ...

g(x) = f(x -h) +k

The translation of f(x) right 1 unit and up 3 units will result in ...

g(x) = f(x -1) +3

Reflection

Reflection of f(x) over the y-axis is accomplished by changing the sign of x:

g(x) = f(-x) . . . . reflection over y-axis

Application

The given g(x) can be obtained a couple of ways. One is ...

  • Translation right 1 and up 3 to get g(x) = f(x -1) +3
  • Reflection over the y-axis to get g(x) = f(-x-1) +3

Doing this reflects the initial right translation to a left translation.

The graph is attached. (The blue curve is g(x).)

__

Alternatively, the given g(x) can be obtained by ...

  • Reflection over the y-axis to get g(x) = f(-x)
  • Translation left 1 and up 3 to get g(x) = f(-(x+1)) +3 = f(-x-1) +3

Since the reflection is done first, the translation is not reflected, but is applied to the reflected function.

The graph of f(x) is given below. State the order of the transformation occurring-example-1
User Ajorquera
by
3.3k points