Understanding Function Transformations

The video tutorial explains how to find an ordered pair on the graph of a translated function, Y = F(X + 4) + 2, given F(2) = -3. It covers the concepts of vertical and horizontal shifts in functions, demonstrating how to translate points on a graph. The tutorial provides a step-by-step explanation of how adding or subtracting constants to the function affects the graph's position. It also offers an alternative approach to understanding these translations, ensuring a comprehensive understanding of the topic.

What does F(2) = -3 imply about the point on the graph of the basic function F(X)?

• The point (2, -3) is on the graph.

• The point (2, 3) is on the graph.

• The point (-2, -3) is on the graph.

• The point (-2, 3) is on the graph.

How does adding a constant D to F(X) affect the graph?

• Shifts the graph down D units.

• Shifts the graph right D units.

• Shifts the graph left D units.

• Shifts the graph up D units.

What happens to the graph of F(X) when you subtract a constant D?

• It shifts left D units.

• It shifts down D units.

• It shifts up D units.

• It shifts right D units.

What is the effect of adding a constant C inside the function, as in F(X + C)?

• Shifts the graph down C units.

• Shifts the graph right C units.

• Shifts the graph left C units.

• Shifts the graph up C units.

If F(X - C) is used, how does the graph shift?

• Up C units.

• Right C units.

• Left C units.

• Down C units.

What is the new X-coordinate when the graph is shifted left by 4 units?

• X = 2

• X = -2

• X = -4

• X = 4

How does adding 2 to the function values affect the graph?

• Shifts the graph up 2 units.

• Shifts the graph down 2 units.

• Shifts the graph right 2 units.

• Shifts the graph left 2 units.

What are the new coordinates of the point after applying the transformations?

• (2, -1)

• (-2, 1)

• (2, 1)

• (-2, -1)

If the input of the new function is +2, what must the X value be?

• X = 4

• X = 2

• X = -2

• X = -4

What is the final Y-coordinate after the transformation?

• Y = -1

• Y = 3

• Y = 1

• Y = -3