Vertex, Range, and Inequalities in Functions

This video tutorial focuses on graphing absolute value functions, covering key concepts such as the axis of symmetry, vertex, transformations, domain, and range. It provides step-by-step instructions for graphing functions like y = |x + 2| and y = |x - 3| + 1 using tables and transformations. The tutorial also explains how to graph absolute value functions with inequalities, including shading regions and determining whether to use solid or dashed lines.

What is the vertex of the function y = |x + 2|?

• (2, 0)

• (0, 2)

• (-2, 0)

• (0, -2)

What is the axis of symmetry for the function y = |x + 2|?

• x = 2

• x = -2

• x = 0

• x = 1

For the function y = |x - 3| + 1, what is the range?

• [1, ∞)

• (-∞, 0]

• (-∞, 1]

• [0, ∞)

How does the graph of y = |x - 3| + 1 shift compared to y = |x|?

• 3 units right, 1 unit down

• 3 units left, 1 unit down

• 3 units right, 1 unit up

• 3 units left, 1 unit up

What is the vertex of the function y = |x + 2| - 3?

• (2, -3)

• (-2, 3)

• (2, 3)

• (-2, -3)

For the inequality y ≥ -2|x - 1| + 4, where should the graph be shaded?

• Below the V

• Above the V

• Outside the V

• Inside the V

What type of line is used for the inequality y ≥ -2|x - 1| + 4?

• No line

• Solid line

• Dashed line

• Dotted line

What is the slope of the function y < 1/3|x + 1| - 2?

• 1/3

• -1/3

• 3

• -3

Where should the graph be shaded for the inequality y < 1/3|x + 1| - 2?

• Above the graph

• Below the graph

• Inside the V

• Outside the V

What is the vertex of the function y < 1/3|x + 1| - 2?

• (1, -2)

• (1, 2)

• (-1, 2)

• (-1, -2)