Find g(x), where g(x) is the translation 5 units down of f(x)=x. Write your answer in the form mx+b, where m and b are integers.

Answer 1

A translation 5 units down means we want to subtract 5.

So if f(x) = x, then g(x) = x - 5

Remember the following for transformations of graphs: y = af(bx + c) + d

1. a = vertical compression (|a| < 1) / vertical stretch (|a| > 1)
2. if a is negative then we have a reflection across the x-axis
3. b = horizontal compression (|b| > 1) / horizontal stretch (|b| < 1)
4. if b is negative then we have a reflection across the y-axis
5. c = horizontal translation (to the right if -c and to the left if +c) aka horizontal shift
6. d = vertical translation (down if -d and up if +d) aka vertical shift