The transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below is Option A; f(x + 4) + 2.
How does transformation of a function happens?
The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
We need to find the transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below.
Assuming there are no vertical or horizontal stretches or any reflections.
Understanding that log base 3 of 1 = 0, that is 3 raised to the 0 power is 1.
Out the transformation, So the coordinate is (1,0).
This has been shifted to the left 2 spots (to -1) and up 3 (to 3),
Therefore we can apply to get the new equation.
f(x + 4) + 2
Thus, it would be a horizontal shift left 2 and a vertical shift up 3.
Therefore, The transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below is Option A; f(x + 4) + 2.
Learn more about transforming functions here:
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