Transformations of Absolute Value Functions

The video tutorial explains how to graph the function f(x) = 2|x + 3| + 2 using a series of transformations. It begins with the basic graph of y = |x| and demonstrates how to shift it left by 3 units, stretch it vertically by a factor of 2, and finally shift it up by 2 units. The tutorial emphasizes understanding these transformations and their effects on the graph, providing a clear step-by-step approach to achieve the final graph of the function.

What is the initial function that is graphed before any transformations?

• y = |x + 3|

• y = |x|

• y = 2|x + 3| + 2

• y = 2|x|

What effect does replacing x with x + 3 have on the graph of y = |x|?

• Shifts the graph to the left by 3 units

• Shifts the graph up by 2 units

• Shifts the graph to the right by 3 units

• Stretches the graph vertically by a factor of 2

Which transformation is responsible for changing the vertex of the graph?

• None of the above

• Vertical shift

• Vertical stretch

• Horizontal shift

How does multiplying the absolute value function by 2 affect the graph?

• It shifts the graph to the left by 2 units

• It shifts the graph up by 2 units

• It stretches the graph vertically by a factor of 2

• It compresses the graph horizontally by a factor of 2

What is the slope of the graph for x values greater than -3 after the vertical stretch?

• -1

• 2

• -2

• 1

What is the slope of the graph for x values less than -3 after the vertical stretch?

• 2

• 1

• -1

• -2

What is the final transformation applied to the function to obtain f(x) = 2|x + 3| + 2?

• Shift the graph to the left by 2 units

• Shift the graph up by 2 units

• Shift the graph to the right by 2 units

• Shift the graph down by 2 units

What is the y-value at x = -3 after all transformations are applied?

• 6

• 4

• 0

• 2

Which of the following sequences of transformations is correct for obtaining the final graph?

• Shift left by 3, stretch vertically by 2, shift up by 2

• Stretch vertically by 2, shift left by 3, shift up by 2

• Shift up by 2, stretch vertically by 2, shift left by 3

• All of the above

What is the final equation of the graph after all transformations?

• y = 2|x + 3|

• y = |x + 3|

• y = 2|x + 3| + 2

• y = |x|