f(x) + n - shift a graph of f n units up
f(x) - n - shift a graph of f n units down
f(x + n) - shift a graph of f n units left
f(x - n) - shift a graph of f n units right.
f(x) = x³, g(x) = (x + 3)³ - 4 = f(x + 3) - 4
3 units left and 4 units down.
(x, y) → (x - 3, y - 4)
therefore
(0, 0) → (0 - 3, 0 - 4) = (-3, -4).
The new point will be equal to (–3, –4).
A parent function in mathematics is the simplest function in a family of functions that keeps the definition of the entire family.
The parent function is
f(x) = x³.
The transformed function is
g(x) = (x+3)³ - 4.
Adding 3 to x before the exponent is applied will translate the function 3 units to the left.
Subtracting 4 from the end of the function will translate the function 4 units down.
Therefore, this means the point (0, 0) will shift to (0-3, 0-4) = (-3, -4).
To learn more about parent function
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