Answer:
h(x) = f(x - 12) - 4
Step-by-step explanation:
The vertex is the turning point (stationary point or minima/maxima) of the graph.
To find the series of translations that transform the graph of y = f(x) onto y = h(x), compare the vertices of both graphs.
Vertices of given functions:
- Vertex of f(x) = (-6, 11)
- Vertex of h(x) = (6, 7)
Differences
- x-values: 6 - (-6) = 12
- y-values: 7 - 11 = -4
Therefore, y = f(x) has been:
- translated 12 units right
- translated 4 units down
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Therefore:
- f(x) translated 12 units right = f(x - 12)
- f(x - 12) translated 4 units down = f(x - 12) - 4
So the formula for h(x) in terms of f(x) is:
h(x) = f(x - 12) - 4
Learn more about transformations here:
brainly.com/question/27845947
