Exploring Horizontal and Vertical Translations in Function Graphs

The video tutorial covers function transformations, focusing on horizontal and vertical shifts. It explains how adding or subtracting constants to the function's input or output affects the graph's position. The tutorial includes examples with absolute value and quadratic functions, demonstrating how to graph these transformations step-by-step.

What is the main focus of the video?

• Graphing functions using horizontal and vertical shifts

• Solving quadratic equations

• Understanding trigonometric functions

• Learning about derivatives

If you add C units to X in the function Y = F(X + C), which direction does the graph shift?

• Left

• Down

• Right

• Up

In the function Y = F(X - C), what happens to the graph?

• It shifts to the left

• It shifts to the right

• It shifts upward

• It shifts downward

What is the Y value of F(X - 1) when X = 3, given F(X) = X^2?

• 1

• 4

• 9

• 16

In the animation, what happens to the blue function when C is set to -2.5?

• It shifts 2.5 units to the left

• It shifts 2.5 units to the right

• It shifts 2.5 units downward

• It shifts 2.5 units upward

What does the function Y = F(X + D) do to the graph?

• Shifts it up D units

• Shifts it down D units

• Shifts it left D units

• Shifts it right D units

If F(X) = X^2, what is the Y value of F(X) - 2 when X = 2?

• 0

• 2

• 6

• 4

How does the function Y = F(X) - D affect the graph?

• Shifts it down D units

• Shifts it up D units

• Shifts it right D units

• Shifts it left D units

What is the parent function of F(X) = |X + 3| + 2?

• X^2

• X^3

• |X|

• 1/X

In the function F(X) = (X - 2)^2 - 4, how is the graph shifted?

• Left 2 units and up 4 units

• Left 2 units and down 4 units

• Right 2 units and down 4 units

• Right 2 units and up 4 units