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)