Understanding Dilation in Functions

This video tutorial explains the concept of dilations in functions, focusing on vertical and horizontal dilations. It provides examples of how to apply these dilations to functions, demonstrating the changes in distance from the x-axis and y-axis. The tutorial also covers enlargements and compressions as combinations of both types of dilations, using algebraic methods to illustrate the transformations.

What is a dilation in the context of functions?

• A reflection of a function

• A translation of a function

• A rotation of a function

• A stretching or compressing of a function

Which of the following is NOT a type of dilation?

• Diagonal dilation

• None of the above

• Horizontal dilation

• Vertical dilation

In a vertical dilation, which axis is the distance increased from?

• Y-axis

• Z-axis

• Origin

• X-axis

How is a vertical dilation by a factor of 'a' achieved?

• Replace Y with aY

• Replace X with aX

• Replace Y with Y/a

• Replace X with X/a

What is the result of vertically dilating the function f(x) = x^2 - 2x by a factor of 3?

• 3x^2 - 2x

• x^2 - 2x

• x^2 - 6x

• 3x^2 - 6x

In a horizontal dilation, which axis is the distance increased from?

• Y-axis

• X-axis

• Origin

• Z-axis

How is a horizontal dilation by a factor of 'b' achieved?

• Replace Y with bY

• Replace X with bX

• Replace Y with Y/b

• Replace X with X/b

What is the result of horizontally dilating the function f(x) = x^2 - 2x by a factor of 3?

• 3x^2 - 2x

• x^2 - 6x

• 9x^2 - 6x

• 1/9x^2 - 2/3x

What are enlargements or compressions in the context of dilations?

• Only vertical dilations

• Only horizontal dilations

• Neither vertical nor horizontal dilations

• Combination of vertical and horizontal dilations

In an enlargement, what remains the same between the original and the enlarged shape?

• Volume

• Area

• Side lengths

• Angles