2.6: Families of Functions

Question 1

Parent Function

Answer 1

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

Question 2

Translation

Answer 2

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

Question 3

Stretch

Answer 3

A vertical —– multiplies all y-values by the same factor greater than 1.

Question 4

Shrink

Answer 4

A vertical —– reduces y-values by a factor between 0 and 1.

Question 5

Reflection

Answer 5

A —– in the x-axis changes y-axis to their opposites.

Question 6

Transformation

Answer 6

Each member of a family of functions is a —–, or change, of a parent function.

Question 7

Parameters

Answer 7

Algebraically, the transformations take the same forme using —–, like h, k, and . Graphically, the results are similar- shifts, stretches, chrinks, and reflections of the parent function.