Mixup of basic function transformations:
– to reflect across the x-axis, take the negative of the function: – f(x)
– to reflect across the y-axis, change the input to -x: f(-x)
– to shift upward vertically by C: add C: f(x) + C
– to shift to the right horizontally by A: replace x by x – A: f(x – A)
Each function g(x) below is a transformation of a basic function f(x). Say what f(x) is, and describe the transformation (sometimes there is more than one transformation). For extra practice graph both g and f on the same set of axes.
1. g(x) = (x – 5)2
2. g(x) = -|x| + 1
3. g(x) = sqrt(-x) (square root of -x)
4. g(x) = 3(x + 1) – 4
5. g(x) = – (x + 1)