Understanding Absolute Value Functions

The video tutorial explains how to graph the absolute value function f(x) = -2|x - 4| + 5. It begins with an introduction to the basic absolute value function, highlighting its V-shape and vertex. The tutorial then demonstrates graphing the function using a table of values, identifying key points such as the vertex and additional points on either side. Finally, it covers graphing the function as a transformation of the basic absolute value function, involving shifts, reflections, and vertical stretches.

What is the first step in graphing the absolute value function F(X) = -2|X - 4| + 5?

• Determine the y-intercept

• Find the slope

• Calculate the derivative

• Use a table of values

What shape do all absolute value function graphs have?

• U shape

• L shape

• V shape

• S shape

What is the vertex of an absolute value function?

• The midpoint of the graph

• The highest or lowest point on the graph

• The point where the graph is horizontal

• The intersection with the y-axis

How do you find the x-coordinate of the vertex for the function F(X) = -2|X - 4| + 5?

• Use the midpoint formula

• Set X equal to 0

• Set the expression inside the absolute value equal to zero

• Find the derivative and set it to zero

What is the y-coordinate of the vertex for the function F(X) = -2|X - 4| + 5?

• 3

• 4

• 5

• 6

What is the y-value when X = 3 for the function F(X) = -2|X - 4| + 5?

• 1

• 3

• 4

• 2

What is the y-value when X = 5 for the function F(X) = -2|X - 4| + 5?

• 3

• 5

• 2

• 4

How does the graph of F(X) = -2|X - 4| + 5 differ from the basic absolute value function?

• It is shifted down and opens down

• It is shifted up and opens up

• It is shifted right and opens down

• It is shifted left and opens up

What transformation occurs when multiplying the absolute value by -2?

• Vertical compression

• Horizontal compression

• Horizontal stretch

• Vertical stretch and reflection across the x-axis

What is the final transformation applied to the graph of F(X) = -2|X - 4| + 5?

• Shift down 5 units

• Shift up 5 units

• Shift right 5 units

• Shift left 5 units