Transformations of Functions

The video tutorial covers the concepts of functions and their transformations, including translations, stretches, and reflections. It explains how to perform horizontal and vertical translations, vertical and horizontal stretches, and reflections across the x-axis and y-axis. The tutorial uses examples to illustrate how these transformations affect the coordinates of a function.

What is the coordinate through which the function passes?

• (2, 2)

• (1, 1)

• (3, 3)

• (4, 4)

If f(2) = 2, what does this imply about the function?

• The function has a maximum at x=2

• The function is undefined at x=2

• The function passes through the point (2, 2)

• The function is decreasing at x=2

What is a translation in the context of functions?

• A reflection of the function

• A scaling of the function

• A shift of the function

• A rotation of the function

How does a horizontal translation of x-2 affect the function?

• Shifts the function 2 units left

• Shifts the function 2 units right

• Shifts the function 2 units up

• Shifts the function 2 units down

What happens to the y-coordinate during a horizontal shift?

• It increases

• It decreases

• It remains unchanged

• It becomes negative

What does adding 3 outside the function bracket indicate?

• A horizontal shift

• A vertical shift

• A reflection

• A stretch

In a vertical shift, what happens to the x-coordinate?

• It becomes negative

• It decreases

• It increases

• It remains unchanged

What is the result of a transformation with x+1 and +4?

• 1 unit left, 4 units down

• 1 unit right, 4 units down

• 1 unit left, 4 units up

• 1 unit right, 4 units up

What is a stretch in the context of functions?

• A reflection of the function

• A scaling of the function

• A shift of the function

• A rotation of the function

How does a vertical stretch by a factor of 3 affect the function?

• Multiplies y-coordinates by 3

• Multiplies x-coordinates by 3

• Divides x-coordinates by 3

• Divides y-coordinates by 3