A) The transformations can be a vertical translation and an horizontal translation.
B) K = 8 and K' = 16
C) g(x) = f(x + 8)
g(x) = f(x) + 16.
Which type of transformation could be used?
A ) By looking at the graph, we see that g(x) can be a translation to the left by K units or up by K' units.
B) In the case the translation is to the left, we can see that it the graph is moved 8 units, so K = 8.
In the case that the translation is up, we can see that it is for 16 units, so we have k' = 16.
C) How to write the equations?
An horizontal translation is written as:
g(x) = f(x + K).
Because the translation is to the left, we have that K is positive, then in our case we have:
g(x) = f(x + 8).
For the vertical translation the formula is:
g(x) = f(x) + K'
In our case, we have:
g(x) = f(x) + 16
If you want to learn more about transformations, you can read:
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