Transformation of functions

Transformation of functions

1. y = f(x)+c

   • shifts the graph of [y = f(x)] c units upward

2. y = f(x)-c

   • shifts the graph of [y = f(x)] c units downward

3. y = cf(x)

   • stretch the graph of [y = f(x)] vertically by a factor of c

4. y = f(x-c)

   • shifts the graph of [y = f(x)] c units to the right

5. y = f(x+c)

   • shifts the graph of [y = f(x)] c units to the left

6. y = (1/c)f(x)

   • shrinks the graph of [y = f(x)] vertically by a factor of c

7. y = f(cx)

   • shrinks the graph of [y = f(x)] horizontally​ by a factor of c

8. y = f(c/x)

   • stretches the graph of [y = f(x)] horizontally​ by a factor of c

9. y = -f(x)

   • reflect the graph of [y = f(x)] about the x-axis

10. y = f(-x)

    • reflect the graph of [y = f(x)] about the y-axis