Function Transformations and Effects

In Unit 5, students explore various function types and their transformations using parameters a, h, and k. The unit covers quadratic functions in vertex form and extends these transformations to other functions, including square root functions. The video explains how a affects vertical dilation, h affects horizontal translation, and k affects vertical translation. It also highlights the inverse relationship between quadratic and square root functions and summarizes the transformations across different function types.

What is the role of 'a' in the transformation of a quadratic function?

• It dilates the graph vertically.

• It reflects the graph over the x-axis.

• It shifts the graph left or right.

• It shifts the graph up or down.

How does 'h' affect the graph of a function?

• It shifts the graph horizontally.

• It shifts the graph vertically.

• It dilates the graph horizontally.

• It reflects the graph over the y-axis.

Which transformation is applied when 'h' is subtracted from x?

• Vertical translation

• Reflection

• Vertical dilation

• Horizontal translation

What is the result of applying a vertical dilation of 2 to a function?

• The graph is compressed vertically by a factor of 2.

• The graph is stretched vertically by a factor of 2.

• The graph shifts 2 units right.

• The graph shifts 2 units up.

In the context of function transformations, what does 'k' do?

• It dilates the graph vertically.

• It reflects the graph over the x-axis.

• It shifts the graph vertically.

• It shifts the graph horizontally.

What is the inverse function of a quadratic function?

• Cubic function

• Exponential function

• Linear function

• Square root function

What is the square root of 9?

• 5

• 4

• 3

• 2

How does 'a' affect the square root function when it is positive?

• It reflects the graph over the y-axis.

• It dilates the graph vertically.

• It shifts the graph horizontally.

• It shifts the graph vertically.

What is the effect of 'h' on the square root function?

• It reflects the graph over the x-axis.

• It shifts the graph horizontally.

• It dilates the graph vertically.

• It shifts the graph vertically.

How does 'k' affect the square root function?

• It reflects the graph over the y-axis.

• It shifts the graph vertically.

• It dilates the graph vertically.

• It shifts the graph horizontally.