Exploring Absolute Value Transformations

This video tutorial covers the process of applying various transformations to functions, focusing on absolute value functions. It explains how negative numbers cause reflections over the x-axis and how stretches affect the graph's shape. The tutorial also discusses identifying the vertex and axis of symmetry, and demonstrates graphing the transformed function step-by-step.

What does a negative number multiplied to the absolute value function cause?

• A reflection over the x-axis

• A shift to the right

• A horizontal compression

• A vertical stretch

What is the parent function for an absolute value function?

• y = |x|

• y = log(x)

• y = x^2

• y = e^x

How do you determine the vertex of the function y = -3|x + 2| - 1?

• (2, 1)

• (2, -1)

• (-2, 1)

• (-2, -1)

What is the axis of symmetry for the function y = -3|x + 2| - 1?

• x = 1

• x = -2

• x = -1

• x = 2

What effect does the number 3 have on the function y = -3|x + 2| - 1?

• It causes a horizontal stretch

• It causes a vertical stretch

• It causes a horizontal compression

• It causes a vertical compression

What does the abbreviation 'rocks' stand for in the context of function transformations?

• Rotation around the origin

• Reflection over the x-axis

• Reflection over the y-axis

• Reflection over the origin

What is the first step in graphing the function y = -3|x + 2| - 1?

• Identify the vertex

• Determine the axis of symmetry

• Plot the y-intercept

• Calculate the slope

At which point does the function y = -3|x + 2| - 1 have its vertex?

• (0, -7)

• (1, -10)

• (-2, -1)

• (-1, -4)

What is the y-coordinate of the function y = -3|x + 2| - 1 at x = 0?

• -1

• -10

• -4

• -7

What happens to the function y = -3|x + 2| - 1 as x moves away from the vertex?

• It shifts upwards

• It becomes narrower

• It becomes wider

• It shifts downwards