AP Precalculus

~ 1.12: Transforming Functions ~

1.12 Course Objectives

Construct a function that is an additive transformation of another function.
Construct a function that is a multiplicative transformation of another function.

The function g (x) = f (x) + k is an additive transformation of the function f that results in a vertical translation of the graph of f by k units.
The function g (x) = f (x + h) is an additive transformation of the function f that results in a horizontal translation of the graph of f by −h units.
The function g ( ) x = a f(x), where a ≠ 0, is a multiplicative transformation of the function f that results in a vertical dilation of the graph of f by a factor of a . If a < 0, the transformation involves a reflection over the x-axis.
The function g (x) = f (bx), where b ≠ 0, is a multiplicative transformation of the function f that results in a horizontal dilation of the graph of f by a factor of |1/b| . If b < 0, the transformation involves a reflection over the y-axis.
Additive and multiplicative transformations can be combined, resulting in combinations of horizontal and vertical translations and dilations.
The domain and range of a function that is a transformation of a parent function may be different from those of the parent function.

The video for AP Precalculus, 1.12: Transforming Functions will come out on Thursday, October 12, 2023.