Chapter 1 | Functions and Graphs
57
Transformation of f ( c >0 )
Effect on the graph of f
f ( x )+ c
Vertical shift up c units
f ( x )− c
Vertical shift down c units
f ( x + c )
Shift left by c units
f ( x − c )
Shift right by c units
Vertical stretch if c >1; vertical compression if 0< c <1
cf ( x )
f ( cx )
Horizontal stretch if 0< c <1; horizontal compression if c >1
− f ( x )
Reflection about the x -axis
f (− x )
Reflection about the y -axis
Table 1.7 Transformations of Functions
Example 1.21 Transforming a Function
For each of the following functions, a. and b., sketch a graph by using a sequence of transformations of a well- known function. a. f ( x ) =− | x +2 | −3 b. f ( x ) =3 − x +1 Solution a. Starting with the graph of y = | x |, shift 2 units to the left, reflect about the x -axis, and then shift down 3 units.
Made with FlippingBook - professional solution for displaying marketing and sales documents online