Graph Transformations and Their Effects

The video tutorial covers four key graph transformations required for the new GCSE curriculum: 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 tutorial also includes practical exercises on sketching transformed graphs, helping students visualize and understand the effects of these transformations.

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

• Reflections and rotations

• Rotations and dilations

• Reflections and translations

• Translations and dilations

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

• It reflects the graph over the y-axis

• It shifts the graph upwards

• It shifts the graph downwards

• It reflects the graph over the x-axis

What happens to the graph when y = f(-x) is applied?

• The graph is reflected over the x-axis

• The graph is shifted to the left

• The graph is shifted to the right

• The graph is reflected over the y-axis

If y = f(x) + a is applied, how is the graph affected?

• The graph is shifted a units to the left

• The graph is shifted a units to the right

• The graph is reflected over the x-axis

• The graph is shifted a units upwards

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

• The graph is shifted a units to the right

• The graph is shifted a units upwards

• The graph is shifted a units to the left

• The graph is reflected over the y-axis

Where does the point (5, 2) move when y = -f(x) is applied?

• (5, -2)

• (-5, 2)

• (5, 2)

• (-5, -2)

How does the point (5, 2) transform under y = f(-x)?

• (5, -2)

• (-5, 2)

• (5, 2)

• (-5, -2)

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

• (5, 4)

• (3, 2)

• (5, 0)

• (7, 2)

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

When sketching y = -f(x), what happens to the parts of the graph above the x-axis?

• They remain unchanged

• They move to the right

• They reflect below the x-axis

• They reflect above the y-axis