Transformations of Functions

This video tutorial explains how to perform transformations on functions, focusing on moving a specific point based on given transformations. It covers horizontal shifts by analyzing the input changes and vertical transformations by applying order of operations. The tutorial demonstrates how to calculate the new coordinates of a point after applying these transformations, resulting in a new point on the transformed graph.

What is the initial point given on the graph of the function?

• (1, 2)

• (0, 0)

• (3, -1)

• (2, -4)

What does subtracting one from the input of a function do to its graph?

• Shifts it right by one unit

• Shifts it left by one unit

• Stretches it vertically

• Reflects it over the x-axis

After the horizontal transformation, what is the new x-coordinate of the point?

• 2

• 1

• 4

• 3

Which transformation affects only the x-coordinate?

• Vertical shift

• Vertical stretch

• Horizontal shift

• Reflection

What effect does multiplying the function by 2 have on the graph?

• No effect

• Reflection

• Vertical stretch

• Horizontal shift

What is the new y-coordinate after the vertical stretch?

• -4

• -8

• -1

• 0

What does subtracting 3 from the function do to the y-values?

• Increases them by 3

• Decreases them by 3

• Doubles them

• Halves them

What is the final y-coordinate after all transformations?

• 0

• -8

• -1

• -4

What is the overall effect of the transformations on the point (2, -4)?

• Moved to (3, -8)

• Moved to (2, -8)

• Moved to (3, -1)

• Moved to (1, -4)

Which of the following is not a transformation discussed in the video?

• Reflection

• Vertical stretch

• Horizontal shift

• Vertical shift