Graph Transformations and Reflections

The video tutorial by Miss Kos covers transformations of functions, including vertical and horizontal translations, dilations, and reflections. It provides examples and calculations to illustrate these concepts, emphasizing the importance of understanding how transformations affect graphs. The tutorial also discusses the relationship between vertical and horizontal dilations and the significance of the parent function in transformations.

What is the result of a vertical translation of f(x) by k units?

• The graph shifts k units down.

• The graph shifts k units up.

• The graph shifts k units to the left.

• The graph shifts k units to the right.

How does a vertical dilation by a factor of a affect the graph of f(x)?

• It shifts the graph vertically.

• It compresses the graph horizontally.

• It stretches the graph vertically.

• It reflects the graph over the y-axis.

What happens to the graph of f(x) when it is reflected over the x-axis?

• The graph is flipped left to right.

• The graph is shifted up.

• The graph is shifted down.

• The graph is flipped upside down.

What is the effect of a horizontal dilation by a factor of 1/b on f(x)?

• The graph is compressed horizontally.

• The graph is stretched horizontally.

• The graph is reflected over the x-axis.

• The graph is reflected over the y-axis.

How does a transformation inside the function affect the x-values?

• It does the opposite of what it appears to do.

• It doubles the x-values.

• It affects the y-values directly.

• It has no effect on the x-values.

In the transformation g(x) = 2f(x) + 3, what does the '+3' indicate?

• A horizontal shift to the left by 3 units.

• A vertical stretch by 3 units.

• A vertical shift up by 3 units.

• A horizontal shift to the right by 3 units.

What does the negative sign in -4f(x) indicate?

• A reflection over the x-axis.

• A reflection over the y-axis.

• A vertical shift down by 4 units.

• A horizontal shift left by 4 units.

Why is the parent function important in transformations?

• It affects the type of transformations possible.

• It has no impact on transformations.

• It determines the color of the graph.

• It only affects vertical transformations.

What is the result of shifting a graph left by 3 units and down by 4 units?

• The graph moves right by 3 units and down by 4 units.

• The graph moves left by 3 units and down by 4 units.

• The graph moves left by 3 units and up by 4 units.

• The graph moves right by 3 units and up by 4 units.

How does a reflection over the x-axis affect a graph?

• It compresses the graph vertically.

• It stretches the graph horizontally.

• It shifts the graph to the right.

• It flips the graph upside down.