Exploring Absolute Value Transformations: Vertical Shifts

The video tutorial explores the effects of adding constants outside the absolute value function, focusing on vertical shifts. It begins by identifying the parent function and determining the vertex and axis of symmetry without graphing. The tutorial then uses a graphing calculator to verify the vertical shift and analyze the graph's behavior, confirming that the function moves up by four units. The video concludes by summarizing the findings and verifying the accuracy of the analysis.

What is the parent function of the absolute value function discussed in the video?

• f(x) = x^2

• f(x) = |x|

• f(x) = x + 4

• f(x) = x - 4

What type of shift occurs when a constant is added outside the absolute value function?

• Diagonal shift

• No shift

• Vertical shift

• Horizontal shift

If a positive constant is added outside the absolute value function, in which direction does the graph shift?

• Right

• Up

• Left

• Down

How can you determine the vertex of the absolute value function without graphing?

• By using a graphing calculator

• By analyzing the constant outside the absolute value

• By examining the constant inside the absolute value

• By looking at the coefficient of x

What is the vertex of the function f(x) = |x| + 4?

• (0, 0)

• (4, 0)

• (4, 4)

• (0, 4)

What is the axis of symmetry for the function f(x) = |x| + 4?

• x = 4

• y = 4

• x = 0

• y = 0

What tool did the instructor use to verify the vertical shift?

• A protractor

• A graphing calculator

• A spreadsheet

• A ruler

How many units did the graph shift up when a +4 was added outside the absolute value function?

• 3 units

• 5 units

• 2 units

• 4 units

What is the shape of the graph of the absolute value function after the transformation?

• Parabola

• Circle

• Line

• V-shape

What is the final vertex of the transformed function discussed in the video?

• (0, 0)

• (0, 4)

• (4, 0)

• (4, 4)