Transformations of Functions

The video tutorial covers the transformation of graphs, focusing on how changes to the function y = f(x) affect the graph's appearance. It explains transformations that alter y-coordinates, such as reflections in the x-axis and vertical shifts, as well as those affecting x-coordinates, like reflections in the y-axis and horizontal shifts. The tutorial includes examples and practice questions to reinforce understanding, and it concludes with a discussion on complex transformations involving simultaneous changes to both x and y coordinates.

What is the original function given in the video?

• y = x - 1 squared

• y = x + 1 squared

• y = x - 1

• y = x^2

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

• It reflects in the y-axis

• It shifts down

• It reflects in the x-axis

• It shifts up

How does the graph change when y = f(x) is transformed to y = f(x) + 2?

• It shifts down by 2 units

• It shifts left by 2 units

• It shifts up by 2 units

• It shifts right by 2 units

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

• It shifts down

• It reflects in the y-axis

• It reflects in the x-axis

• It shifts up

If the graph of y = f(x) has a minimum point at (1, -2), what is the minimum point of y = -f(x)?

• (-1, 2)

• (1, -2)

• (-1, -2)

• (1, 2)

For the transformation y = f(x - 2), what happens to the x-coordinates?

• Subtract 2 from x-coordinates

• Divide x-coordinates by 2

• Multiply x-coordinates by -1

• Add 2 to x-coordinates

What is the result of applying the transformation y = f(x + 3) to the x-coordinates?

• Divide x-coordinates by 3

• Add 3 to x-coordinates

• Subtract 3 from x-coordinates

• Multiply x-coordinates by -1

If a point (3, -5) on the original graph is transformed by y = -f(x + 3), what are the new coordinates?

• (0, 5)

• (6, -5)

• (0, -5)

• (3, 5)