Understanding Function Transformations

This video tutorial on AP Precalculus covers function transformations, including additive and multiplicative types. It explains vertical and horizontal translations and dilations, and how these transformations affect the graph of a function. The tutorial also discusses combining transformations and their impact on domain and range. Practice problems are provided to reinforce learning.

What is the primary focus of the AP Precalculus course as introduced in the video?

• Function transformations

• Trigonometric identities

• Polar functions

• Complex numbers

What type of transformation is described by g(x) = f(x) + k?

• Vertical dilation

• Horizontal dilation

• Horizontal translation

• Vertical translation

If a function is transformed by g(x) = f(x - 5), in which direction does the graph move?

• 5 units down

• 5 units up

• 5 units to the right

• 5 units to the left

Which transformation moves the graph of f(x) by k units left or right?

• Horizontal dilation

• Vertical dilation

• Horizontal translation

• Vertical translation

What happens to a graph when it undergoes a vertical dilation with a negative factor?

• It reflects over the x-axis

• It shifts upwards

• It reflects over the y-axis

• It shifts downwards

In a vertical dilation, what effect does increasing the dilation factor have on the graph?

• The graph becomes wider

• The graph becomes narrower

• The graph shifts right

• The graph shifts left

What is the effect of a negative factor in a vertical dilation?

• The graph shifts upwards

• The graph shifts downwards

• The graph reflects over the x-axis

• The graph reflects over the y-axis

What happens to the graph of a function when a is negative in a vertical dilation?

• It reflects over the x-axis

• It reflects over the y-axis

• It shifts upwards

• It shifts downwards

What is the result of a horizontal dilation with a factor of 1/B when B is negative?

• Horizontal translation

• Reflection over the y-axis

• Vertical translation

• Reflection over the x-axis

How does a horizontal dilation affect the graph of a function?

• It stretches or compresses the graph horizontally

• It stretches or compresses the graph vertically

• It shifts the graph up or down

• It shifts the graph left or right