Translating, Reflecting and Stretching Graphs

1. The graph of f(x) = x² - 4x is shown in each of the four figures below.
In each of the parts a - d, a function g is also given.
i) Describe the transformation which will change the graph of f into the graph of g.
ii) Sketch the graph of g.

(a)	(b)
i) Describe the transformation which transform the graph of f(x) = x2 - 4x into the graph of g(x) = x2 - 4x +3.	i) Describe the transformation which transform the graph of f(x) = x2 - 4x into the graph of g(x) = (x+2)2 - 4(x+2).
ii) Sketch the graph of g on the coordinate system provided above.	ii) Sketch the graph of g on the coordinate system provided above.

(c)	(d)
i) Describe the transformation which transform the graph of f(x) = x2 - 4x into the graph of g(x) = -(x2 - 4x).	i) Describe the transformation which transform the graph of f(x) = x2 - 4x into the graph of g(x) = 1/2.(x2 - 4x).
ii) Sketch the graph of g on the coordinate system provided above.	ii) Sketch the graph of g on the coordinate system provided above.

2. Four transformations graph of f(x) = x³-2x² + 1 are shown below.

i) Describe the transformation which will change f into g.
ii) Write the equation for g and express it in simplified form..

(a)	(b)
(c)	(d)

3. The graph of y = f(x) is shown in each of the four figures below.
In each of the parts a - d, a new function is formed from f.
i) Describe the transformation which will change the graph of f into the graph the new function..
ii) Sketch the graph of this new function.

a) y = f(x) + 2	b) y = f(x+2)
c) y = 1- f(x)	d) y = 1/2. f(x)