Graph Transformations and Their Effects

This video tutorial covers the four key transformations of graphs at the GCSE level: reflection in the x-axis (y = -f(x)), reflection in the y-axis (y = f(-x)), vertical translation (y = f(x) ± a), and horizontal translation (y = f(x ± a)). Each transformation is explained with examples, showing how points on the graph are affected. The video also includes practical examples and sketches to illustrate these transformations.

What are the four types of graph transformations discussed in the video?

• Reflections and rotations

• Reflections and translations

• Translations and dilations

• Rotations and dilations

What happens to a graph when it undergoes the transformation y = -f(x)?

• It shifts vertically

• It reflects over the x-axis

• It reflects over the y-axis

• It shifts horizontally

How does the transformation y = f(-x) affect a graph?

• It shifts horizontally

• It reflects over the y-axis

• It shifts vertically

• It reflects over the x-axis

What is the effect of the transformation y = f(x) + a on a graph?

• It shifts the graph a units to the right

• It shifts the graph a units up

• It shifts the graph a units to the left

• It shifts the graph a units down

If a graph is transformed by y = f(x - a), in which direction does it move?

• a units up

• a units to the right

• a units down

• a units to the left

When a point (5, 2) is transformed by y = -f(x), where does it move?

• (-5, -2)

• (-5, 2)

• (5, -2)

• (5, 2)

Under the transformation y = f(-x), where does the point (5, 2) move?

• (5, 2)

• (-5, 2)

• (5, -2)

• (-5, -2)

What is the new position of the point (5, 2) after the transformation y = f(x) + 2?

• (3, 2)

• (5, 0)

• (7, 2)

• (5, 4)

In the context of graph transformations, what does sketching involve?

• Drawing the transformed graph only

• Drawing the original graph only

• Drawing both the original and transformed graphs

• Drawing graphs without transformations

How does the transformation y = -f(x) affect the sketch of a graph?

• It reflects the graph over the x-axis

• It shifts the graph horizontally

• It reflects the graph over the y-axis

• It shifts the graph vertically