Transformations of Piecewise-Defined Functions

This video tutorial covers transformations of piecewise defined functions, focusing on absolute value functions. It explains how to reflect graphs over the x-axis, perform vertical and horizontal shifts, and apply vertical stretches and compressions. The tutorial also demonstrates how to analyze graphs with multiple transformations and identify transformations without visual aids.

What type of functions are the focus of this lesson?

• Exponential functions

• Polynomial functions

• Piecewise defined functions

• Quadratic functions

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What does a negative coefficient in front of the absolute value symbol indicate?

• Reflection over the x-axis

• Vertical stretch

• Horizontal shift

• Vertical shift

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How is a reflection over the x-axis represented in a function?

• By dividing the function by a negative number

• By adding a number after the absolute value

• By subtracting a number inside the absolute value

• By multiplying the function by a negative number

How does adding a number after the absolute value symbol affect the graph?

• Horizontal shift

• Reflection over the y-axis

• Vertical shift

• Vertical stretch

What does adding a number outside the absolute value symbol in a function do?

• Indicates a vertical stretch

• Indicates a reflection over the y-axis

• Causes a vertical shift

• Causes a horizontal shift

What does a positive number inside the absolute value symbol (subtracted from x) cause?

• Shift to the left

• Vertical compression

• Vertical stretch

• Shift to the right

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What is the result of a horizontal shift to the left in the function's graph?

• Subtracting a number inside the absolute value

• Adding a negative number inside the absolute value

• Multiplying by a negative number

• Adding a positive number inside the absolute value

Which transformation does not affect the vertex's x-coordinate?

• Vertical shift

• Horizontal shift

• Reflection over the x-axis

• Vertical stretch

What indicates a vertical stretch in a graph?

• A coefficient greater than 1

• A negative coefficient

• A coefficient less than 1

• A positive integer added to the function

What transformation does a coefficient less than 1 but greater than 0 indicate?

• Vertical stretch

• Horizontal shift

• Vertical compression

• Reflection over the x-axis