Translations and Reflections of Graphs

The video tutorial covers the concepts of graph translations and reflections. It explains how translations involve shifting a graph horizontally or vertically by altering the function's equation. Vertical shifts affect the Y coordinate, while horizontal shifts affect the X coordinate, often in the opposite direction of intuition. The tutorial also discusses reflections, which involve flipping the graph over the X or Y axis by modifying the function's equation. These transformations are crucial for understanding how graphs behave under different mathematical operations.

What happens to a graph when you add a value outside the function F(x)?

• It shifts vertically.

• It shifts horizontally.

• It reflects over the X-axis.

• It reflects over the Y-axis.

If you add a value inside the brackets of F(x), in which direction does the graph shift?

• In the same direction as the value added.

• It does not shift.

• In the opposite direction to the value added.

• It reflects over the X-axis.

In the example F(x) - 3 + 5, what is the resulting shift of the graph?

• 3 units down, 5 units left

• 3 units up, 5 units right

• 3 units right, 5 units up

• 3 units left, 5 units down

What effect does changing F(x) to -F(x) have on the graph?

• It shifts the graph downwards.

• It reflects the graph over the X-axis.

• It reflects the graph over the Y-axis.

• It shifts the graph upwards.

How does reversing the inputs of a function affect the graph?

• It reflects the graph over the Y-axis.

• It reflects the graph over the X-axis.

• It shifts the graph to the right.

• It shifts the graph to the left.