Answer:
- translation right 1 and up 3
- reflection over the y-axis
- see the attachment for a graph
Step-by-step 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).)
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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.
