2.6:Families of Functions

Question 1

Parent Function

Answer 1

The simplest function with these characteristics. The equations of the functions in a family resemble each other. So do the graphs. Offspring of parent functions include translations, stretches, and shrinks.

Question 2

Translation

Answer 2

Shifts a graph horizontally, vertically. or both. It results in a graph of the same shape and size but possibly in a different position.

Question 3

Stretch

Answer 3

A vertical stretch multiplies all y-values by the same factor greater than 1, thereby stretching a graph vertically.

Question 4

Shrink

Answer 4

A vertical shrink reduces y-values by a factor between 0 and 1, thereby compressing the graph vertically.

Question 5

Reflection

Answer 5

A reflection in the x-axis changes y-values to their opposites. When you change the y-values of a graph to their opposites, the graph reflects across the x-axis.

Question 6

Transformation

Answer 6

Each member of a family is a transformation, or change, of a parent function.

Question 7

Parameter

Answer 7

Algebraically, the transformations take the same form using parameters, like h, k, and a.