Function Transformations and Characteristics

This video tutorial covers the basics of parent functions and their transformations. It begins with an introduction to four types of parent functions: constant, linear, absolute value, and quadratic. The video then explains transformations, focusing on translations and reflections. Vertical and horizontal translations are discussed in detail, including examples of shifting functions up, down, left, and right. The tutorial concludes with an explanation of reflections over the x-axis and y-axis, illustrating how these transformations affect the orientation of functions.

What is the simplest form of a family of functions called?

• Cousin functions

• Sibling functions

• Parent functions

• Child functions

What is the parent function of all constant functions?

• f(x) = 1

• f(x) = |x|

• f(x) = x^2

• f(x) = x

What is the graphical representation of constant functions?

• Vertical lines

• Horizontal lines

• Diagonal lines

• Curved lines

What is the parent function of linear functions?

• f(x) = x

• f(x) = |x|

• f(x) = 1

• f(x) = x^2

What is a key characteristic of linear functions?

• Infinite slope

• No slope

• Variable slope

• Constant slope

What is the parent function of absolute value functions?

• f(x) = x

• f(x) = |x|

• f(x) = 1

• f(x) = x^2

What shape do absolute value functions form on a graph?

• U-shaped

• V-shaped

• S-shaped

• L-shaped

What is the parent function of quadratic functions?

• f(x) = |x|

• f(x) = 1

• f(x) = x^2

• f(x) = x

What shape do quadratic functions form on a graph?

• S-shaped

• V-shaped

• L-shaped

• U-shaped

What are transformations in the context of functions?

• Ways to create new functions

• Ways to alter or manipulate functions

• Ways to delete functions

• Ways to duplicate functions