Understanding Absolute Value Functions

The video tutorial explains how to graph the absolute value function f(x) = 1/2 |x + 2| - 3. It covers the basic shape of absolute value functions, the importance of the vertex, and how to select X values for graphing. The tutorial also demonstrates evaluating the function to find corresponding Y values and graphing the function using transformations. Key concepts include understanding the vertex, choosing appropriate X values, and applying transformations to graph the function accurately.

What is the general shape of an absolute value function graph?

• A circle

• A parabola

• A straight line

• A V shape

What is the vertex of an absolute value function?

• The point where the graph crosses the x-axis

• The point where the graph crosses the y-axis

• The highest or lowest point on the graph

• The midpoint of the graph

How do you find the x-coordinate of the vertex for the function f(x) = 1/2 |x + 2| - 3?

• Set x = 2

• Set x - 3 = 0

• Set x = 0

• Set x + 2 = 0

Why is it beneficial to choose x-values that make x + 2 a multiple of 2?

• To avoid negative y-values

• To make the graph steeper

• To ensure the graph is symmetrical

• To simplify calculations and avoid fractions

What is the y-value when x = -2 for the function f(x) = 1/2 |x + 2| - 3?

• 2

• 0

• -1

• -3

Which point is not on the graph of the function f(x) = 1/2 |x + 2| - 3?

• (-2, -3)

• (0, -2)

• (-4, -2)

• (2, 0)

What is the significance of the vertex in graphing an absolute value function?

• It is the point where the graph intersects the y-axis

• It determines the slope of the graph

• It is the point where the graph changes direction

• It is the midpoint of the graph

How does the graph of f(x) = 1/2 |x + 2| - 3 differ from the basic absolute value function?

• It is shifted right 2 units and up 3 units

• It is shifted left 2 units and down 3 units

• It is shifted right 2 units and down 3 units

• It is shifted left 2 units and up 3 units

What effect does multiplying the absolute value function by 1/2 have on the graph?

• It stretches the graph vertically

• It compresses the graph horizontally

• It shifts the graph upwards

• It shifts the graph downwards

What transformation occurs when you add 2 inside the absolute value function?

• The graph shifts right 2 units

• The graph shifts up 2 units

• The graph shifts left 2 units

• The graph shifts down 2 units