Parent Functions and Transformations 2 7 Parent Functions

Parent Functions and Transformations 2. 7

Parent Functions • A family of graphs is a group of graphs that display one or more similar characteristics. • The parent function is the simplest of the graphs.

Transformations Translation: Moves a figure up, down, left, or right. • When a constant k is added or subtracted from the parent function it moves up or down. • Ex) f(x) = |x| + 5 • When a constant h is added or subtracted from the parent function it moves left or right. • Ex) f(x) = |x + 5|

Transformations Reflection: flips a figure over a line called the line of reflection. • When the parent function is multiplied by -1, the result –f(x) is a reflection in the x-axis. • Ex) f(x) = -|x|

Transformations Dilation: Shrinks or enlarges a figure. Graph gets narrow Ex) f(x) = 3|x | Graph gets wider Ex) f(x) = 1/2|x |

Example 1 Describe the transformation in y = |x + 1|. Then graph the function. The graph of the function is a translation of 1 unit to the left.

Example 2 Describe the transformation in y = –x 2. Then graph the function. The graph of the function is a reflection across the x-axis.

Example 3 Makes it wider

Example 5 Write an equation for the function. f(x) = (x – 3)2 + 1

Example 6 Describe the transformation in the function. – 2 translates the graph down 2 units reflects the graph across the x-axis and makes the graph wider. +4 translates the graph left 4 units