Graphing Absolute Value Functions: A Deep Dive

This video tutorial explains how to graph a nonlinear absolute value function. It covers the basic V-shape of the function and how to apply transformations such as horizontal and vertical shifts. The tutorial details how to determine the vertex and axis of symmetry, and provides guidance on plotting points and drawing the graph accurately. The function is shifted left by two units and down by three units, and the process is mirrored on both sides of the axis of symmetry to maintain the V-shape.

What type of function is being graphed in this video?

• Linear function

• Quadratic function

• Exponential function

• Absolute value function

What is the basic shape of an absolute value function?

• A circle

• A V-shape

• A parabola

• A straight line

What does the plus two inside the absolute value function indicate?

• Move the graph to the right two units

• Move the graph up two units

• Move the graph down two units

• Move the graph to the left two units

What does the minus three at the end of the function indicate?

• Move the graph to the left three units

• Move the graph up three units

• Move the graph down three units

• Move the graph to the right three units

Where does the vertex of the absolute value function start before any adjustments?

• (2, -3)

• (-2, -3)

• (1, 1)

• (0, 0)

After shifting, what are the new coordinates of the vertex?

• (0, 0)

• (2, 3)

• (-3, -2)

• (-2, -3)

What is the understood coefficient of the absolute value function if not explicitly written?

• -1

• 1

• 2

• 0

What is the role of the coefficient in the absolute value function?

• It determines the slope

• It determines the horizontal shift

• It determines the vertex

• It determines the vertical shift

What is the axis of symmetry in the context of the absolute value function?

• A vertical line through the vertex

• A horizontal line through the vertex

• A diagonal line through the vertex

• A curved line through the vertex

What should be added to the ends of the graph to indicate it continues indefinitely?

• Circles

• Arrows

• Dots

• Lines