Graph Transformations and Reflections

This video tutorial covers four types of transformations on a given function's graph: vertical shift, reflection across the x-axis, horizontal shift, and reflection across the y-axis. Each transformation is explained with examples, showing how to adjust the coordinates of key points to achieve the desired graph. The tutorial emphasizes understanding the effects of adding or subtracting constants to the function's equation and changing the signs of coordinates.

What happens to the graph of a function when a constant is added to the y-coordinates?

• The graph shifts downwards.

• The graph shifts to the left.

• The graph shifts upwards.

• The graph shifts to the right.

What happens to the graph of f(x) when you add a constant to the function's output?

• It shifts to the right.

• It shifts downwards.

• It shifts upwards.

• It shifts to the left.

If g(x) = -f(x), what transformation occurs to the graph of f(x)?

• It shifts down.

• It shifts up.

• It reflects across the x-axis.

• It reflects across the y-axis.

How do you achieve a leftward shift of a graph by 3 units?

• Subtract 3 from the y-coordinates.

• Add 3 to the y-coordinates.

• Subtract 3 from the x-coordinates.

• Add 3 to the x-coordinates.

In the transformation g(x) = f(x + c), what does a positive c value indicate?

• The graph shifts left.

• The graph shifts right.

• The graph shifts up.

• The graph shifts down.

What is the result of subtracting a constant from the x-coordinates of a function?

• The graph shifts left.

• The graph reflects across the y-axis.

• The graph shifts right.

• The graph reflects across the x-axis.

If g(x) = f(x - 3), what is the transformation applied to f(x)?

• Shift up by 3 units.

• Shift down by 3 units.

• Shift right by 3 units.

• Shift left by 3 units.

What is the effect of changing the sign of the x-coordinates in a function?

• The graph shifts upwards.

• The graph shifts downwards.

• The graph reflects across the x-axis.

• The graph reflects across the y-axis.

When g(x) = f(-x), what transformation is applied to f(x)?

• It shifts up.

• It reflects across the y-axis.

• It reflects across the x-axis.

• It shifts down.

What is the effect of reflecting a graph across the y-axis?

• The graph shifts up.

• The y-coordinates are negated.

• The x-coordinates are negated.

• The graph shifts down.