Translations , Reflections ,Stretches And Compression

Translations of functions

Suppose that y = f(x)  is a function and c is a positive constant.
Then the graph of,

a) y = f(x)+c is the graph of f shifted vertically Up  c units.
b) y = f(x)-c is the graph of f shifted vertically Down  c units.
c) y = f(x+c) is the graph of f shifted horizontally to the left  c units.
d) y = f(x-c) is the graph of f shifted horizontally to the right  c units.

Show figure 1 :





Reflections of function:

Suppose that y = f(x)  is a function. Then the graph of ,

1) y = -f(x) is the graph of f reflected in the x=axis.
2) y = f(-x) is the graph of f reflected in the y=axis.

Show figure 2

Stretches And Compression : 

Suppose that y = f(x)  is a function and c is a positive constant.
Then the graph of,

1) y =c f(x) is the graph of f
            i) vertically stretched by a factor of c if c > 1
           ii) vertically compressed by a factor of (1/c) if  0 < c < 1.
2) y = f(cx) is the graph of f
            i) horizontally  stretched by a factor of (1/c) if  0 < c < 1.
           ii) horizontally compressed by a factor of c if c > 1.

Show figure 2