Graph Transformations and Functions

The video tutorial covers family functions, focusing on parent functions and their transformations, including translations, stretches, and shrinks. It explains how these transformations affect the graph of functions, particularly absolute value functions, and demonstrates the use of GeoGebra for visualizing these changes.

What is a family function?

• A function that includes only linear functions.

• A function that includes only parent functions.

• A function that includes parent functions and their transformations.

• A function that includes only offspring functions.

Which of the following is the simplest form of a linear function?

• y = 2x + 3

• y = 3x - 2

• y = x

• y = x + 1

What happens to the graph of y = |x| when a vertical translation of -3 is applied?

• The graph shifts 3 units up.

• The graph shifts 3 units down.

• The graph shifts 3 units to the right.

• The graph shifts 3 units to the left.

How does a horizontal translation affect the graph of a function?

• It shrinks the graph horizontally.

• It stretches the graph vertically.

• It shifts the graph left or right.

• It shifts the graph up or down.

What is the effect of a stretch on a graph?

• It shifts the graph horizontally.

• It shifts the graph vertically.

• It changes the slope of the graph.

• It flips the graph across the x-axis.

What does a reflection do to a graph?

• It shifts the graph vertically.

• It shifts the graph horizontally.

• It flips the graph across an axis.

• It stretches the graph.

Which term describes the simplest function within a family of functions?

• Offspring function

• Parent function

• Translation

• Reflection