Question

Explain the transformation rules for the graph of y=2|x-2|+5

Answer 1

1) Graph f(x) = |x|

Observe that y = 2|x - 2| + 5 = 2f(x) + 5

So, these are the transformation rules that you can use:

2) shift the graph 2 units to the rigth: because |x - 2| is f(x - 2)

3) dilate the function (stretch vertically) multiplying by 2

4) shift the graph 5 units upward: because adding a constant to the function moves the graph upward the same amount of units as the value of the constant.